Gch1 l1
•Download as PPT, PDF•
0 likes•318 views
This document is from a geometry textbook and covers key concepts about points, lines, and planes. It defines these basic geometric objects as undefined terms that cannot be defined using other objects. It discusses properties like collinear points, coplanar points, segments, rays, and intersections. Examples demonstrate naming, drawing, and identifying these objects and their relationships based on basic postulates about points, lines and planes. The lesson aims to establish understanding of the fundamental building blocks of geometry.
Report
Share
Report
Share
Recommended
1 4 geometry postulates
This document defines basic geometric terms like point, line, and plane. It explains that a point is a location, a line is a series of points that extends in two directions, and a plane is a flat surface that contains lines and points. The document also lists four postulates of geometry: (1) Through any two points there is exactly one line, (2) If two lines intersect, they intersect at one point, (3) If two planes intersect, they intersect at one line, and (4) Through any three noncollinear points there is exactly one plane. It provides examples of naming planes and lines using these definitions.
Postulates (Geometry 1_3)
This document discusses geometry postulates, which are basic statements accepted as true without proof. It provides four postulates:
1) Two points determine a unique line.
2) If two lines intersect, their intersection is a point.
3) Three noncollinear points determine a unique plane.
4) If two planes intersect, their intersection is a line.
The document then provides examples of applying these postulates to identify lines and planes given certain points.
GEOMETRY INTRODUCTION
This document defines and discusses basic geometric concepts such as points, lines, planes, segments, rays, and their relationships. It provides examples of naming and drawing these concepts, and defines terms like collinear, coplanar, and intersections. The key topics covered are that a point has no size, a line extends infinitely in both directions, and a plane extends infinitely in all directions.
GEOMETRY
This document is a lesson on understanding points, lines, and planes in geometry from Holt McDougal Geometry. It includes examples of naming and drawing points, lines, segments, rays, and planes. It also defines key terms like collinear, coplanar, and postulates. The lesson explains that points, lines, and planes are the basic undefined terms in geometry and discusses properties like intersections and representations of intersections between geometric figures.
Math 7 geometry 02 postulates and theorems on points, lines, and planes
This document covers basic concepts in geometry including:
1. Definitions, undefined terms, postulates, and theorems related to points, lines, and planes. Undefined terms include points, lines, and planes. Definitions clearly define concepts like line segments.
2. Postulates are statements accepted as true without proof, including the ruler postulate, segment addition postulate, and plane postulate.
3. Theorems are important statements that can be proven, such as the intersection of lines theorem and the theorem regarding a line and point determining a unique plane.
Geometry unit 1.2
This document provides an introduction to points, lines, and planes in geometry. It defines key terms like point, line, segment, ray, and plane. It provides examples of naming and drawing different geometric shapes involving these concepts, like naming coplanar points, drawing segments between two endpoints, and representing the intersection of lines and planes. The document emphasizes that points, lines, and planes are basic undefined terms in geometry and introduces concepts like collinear points, coplanar points, and using dashed lines to represent hidden parts of figures.
1 5 Postulates And Theorems Relating Points, Lines Filled In
The document outlines several postulates and theorems relating points, lines, and planes in geometry:
Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane.
Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane.
Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2
Geometry lesson
This document provides a lesson on geometry for grades 9-11 that includes:
1) Discussing California geometry standards and writing geometric proofs, including proofs by contradiction.
2) An example of a warm up exercise involving making conclusions from given geometry statements.
3) The five essential parts of a proof: stating the theorem, given information, drawing a diagram, stating what is to be proved, and developing the proof using deductive reasoning.
Recommended
1 4 geometry postulates
This document defines basic geometric terms like point, line, and plane. It explains that a point is a location, a line is a series of points that extends in two directions, and a plane is a flat surface that contains lines and points. The document also lists four postulates of geometry: (1) Through any two points there is exactly one line, (2) If two lines intersect, they intersect at one point, (3) If two planes intersect, they intersect at one line, and (4) Through any three noncollinear points there is exactly one plane. It provides examples of naming planes and lines using these definitions.
Postulates (Geometry 1_3)
This document discusses geometry postulates, which are basic statements accepted as true without proof. It provides four postulates:
1) Two points determine a unique line.
2) If two lines intersect, their intersection is a point.
3) Three noncollinear points determine a unique plane.
4) If two planes intersect, their intersection is a line.
The document then provides examples of applying these postulates to identify lines and planes given certain points.
GEOMETRY INTRODUCTION
This document defines and discusses basic geometric concepts such as points, lines, planes, segments, rays, and their relationships. It provides examples of naming and drawing these concepts, and defines terms like collinear, coplanar, and intersections. The key topics covered are that a point has no size, a line extends infinitely in both directions, and a plane extends infinitely in all directions.
GEOMETRY
This document is a lesson on understanding points, lines, and planes in geometry from Holt McDougal Geometry. It includes examples of naming and drawing points, lines, segments, rays, and planes. It also defines key terms like collinear, coplanar, and postulates. The lesson explains that points, lines, and planes are the basic undefined terms in geometry and discusses properties like intersections and representations of intersections between geometric figures.
Math 7 geometry 02 postulates and theorems on points, lines, and planes
This document covers basic concepts in geometry including:
1. Definitions, undefined terms, postulates, and theorems related to points, lines, and planes. Undefined terms include points, lines, and planes. Definitions clearly define concepts like line segments.
2. Postulates are statements accepted as true without proof, including the ruler postulate, segment addition postulate, and plane postulate.
3. Theorems are important statements that can be proven, such as the intersection of lines theorem and the theorem regarding a line and point determining a unique plane.
Geometry unit 1.2
This document provides an introduction to points, lines, and planes in geometry. It defines key terms like point, line, segment, ray, and plane. It provides examples of naming and drawing different geometric shapes involving these concepts, like naming coplanar points, drawing segments between two endpoints, and representing the intersection of lines and planes. The document emphasizes that points, lines, and planes are basic undefined terms in geometry and introduces concepts like collinear points, coplanar points, and using dashed lines to represent hidden parts of figures.
1 5 Postulates And Theorems Relating Points, Lines Filled In
The document outlines several postulates and theorems relating points, lines, and planes in geometry:
Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane.
Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane.
Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2
Geometry lesson
This document provides a lesson on geometry for grades 9-11 that includes:
1) Discussing California geometry standards and writing geometric proofs, including proofs by contradiction.
2) An example of a warm up exercise involving making conclusions from given geometry statements.
3) The five essential parts of a proof: stating the theorem, given information, drawing a diagram, stating what is to be proved, and developing the proof using deductive reasoning.
1 1 understanding points, lines, & planes
This document is from a Holt Geometry textbook and covers key concepts about points, lines, and planes. It defines points, lines, and planes as undefined terms that are building blocks of geometry. It discusses properties such as collinear points on a line, coplanar points on a plane, and intersections between lines and planes. Examples demonstrate naming and drawing points, lines, segments, rays, and planes as well as representing intersections between geometric figures.
Geometry lesson
This geometry lesson document introduces key concepts about points, lines, and planes. It defines points, lines, and planes as the basic undefined terms or building blocks of geometry. It discusses properties such as collinear points that lie on the same line, and coplanar points that lie on the same plane. The document provides examples of naming and drawing points, lines, segments, rays, and planes. It also covers basic facts about intersections of lines and planes.
Properties of Geometric Figures
This document defines key geometric terms and concepts including:
- Collinear points which lie on the same line. Coplanar points which lie on the same plane.
- Five postulates outline the fundamental properties of points, lines, and planes: any two points define a single unique line; a plane contains at least three non-collinear points; any three points lie in a single plane; intersecting lines or planes meet at a point or line.
- Theorems describe relationships between lines and planes, such as two intersecting lines lying in a single plane, or a line and point not on the line defining a unique plane.
Introduction to coordinate geometry
Any point on a plane can be named with two numbers called coordinates - an x-coordinate for the distance from the origin along the x-axis and a y-coordinate for the distance along the y-axis. The coordinate grid is divided into four quadrants by the x and y axes, and points can be plotted in the grid and identified by their coordinates and quadrant. Linear equations can be graphed by making a table of solutions and plotting the points, then drawing a straight line through them.
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeks
This document provides an introduction to mathematics concepts for direct3D game programming, including:
- 2D rotation formulas for rotating a point about an angle
- Definitions of domain, codomain, exponentiation, factorial, square root, and cubic root
- Explanations of inverse functions, Pythagorean theorem, summation notation, and practice problems for various concepts
- Overviews of the Cartesian coordinate system, trigonometric functions, and how to implement them in programs
Ac1.2gMorePracticeProblems
More practice with naming points, lines and planes and observing what is going on in diagrams. This is for high school students
Points, Lines and Planes
This document defines key geometry concepts such as points, lines, planes, and their relationships. It provides examples of naming points, lines, and planes, including collinear points that lie on the same line and coplanar points that lie in the same plane. Examples also demonstrate naming segments and rays with different endpoints, and identifying opposite rays. Diagrams show intersecting lines and planes, including lines within a plane, lines that do not intersect a plane, and lines intersecting a plane at a point. Two intersecting planes are shown meeting at a line of intersection. Guided practice problems apply the concepts to name intersections and identify relationships in diagrams.
1 2 Points, Lines, And Planes
This document defines and explains basic geometric terms and postulates. It defines a point as having no size and being represented by a dot. It defines a line as a series of points that extends in two opposite directions without end. It defines a plane as a flat surface that extends infinitely in length and width, having no thickness. It states postulates such as through any two points there is exactly one line, if two lines intersect they intersect at exactly one point, and if two planes intersect they intersect at exactly one line.
Basics Of Geometry 1
The document introduces some basic concepts in geometry, including:
1. Points, lines, and planes are undefined terms that form the foundations of geometry.
2. It explains concepts like collinear points, coplanar points, line segments, rays, and how to classify angles.
3. It discusses intersections of lines, planes, and examples of modeling intersections of geometric figures.
1.2 Ruler Postulates
The document discusses three geometric postulates:
1) The ruler postulate establishes a one-to-one correspondence between points on a line and real numbers on the number line, where the distance between points equals the absolute value of the difference of their corresponding numbers.
2) The ruler placement postulate allows choosing a number line such that two given points correspond to 0 and a positive number.
3) The segment addition postulate states that if one point is between two others, the sum of the distances to the end points equals the distance between the outer points.
GEOMETRY: POINTS, LINES. PLANE
By this end of the presentation you will be able to:
Identify and model points, lines, and planes.
Identify collinear and coplanar points.
Identify non collinear and non coplanar points.
Topic 1. points, line and plane
The three undefined terms in geometry are point, line, and plane. A point indicates a position in space and is named with capital letters or coordinates. A line is an infinite set of adjacent points that extends in both directions, named using two points or a lowercase letter. A plane is a flat surface that extends indefinitely in all directions, named using three points or an uppercase letter.
Language of Geometry
This document introduces basic geometric concepts including points, lines, and planes. It defines these terms and provides examples of representing them visually. Key points covered include:
- A point has no dimension and is represented by a dot.
- A line consists of infinitely many points and is shown as an arrowed line.
- A plane is a flat, thickness-less surface that extends indefinitely in all directions and is usually pictured as a four-sided shape.
- Coplanar and collinear points are defined in relation to lying on the same plane or line, respectively.
Math14 lesson 5
The document discusses different types of equations that can represent straight lines in a plane, including point-slope form, two-point form, slope-intercept form, and normal form. It provides examples of writing the equation of a line given characteristics like two points, slope and intercept, or being parallel/perpendicular to another line. The document also covers topics like finding the distance from a point to a line and the equations of angle bisectors.
1.2 points, lines and planes
This document provides lesson material on classifying and naming geometric figures such as points, lines, planes, segments, rays, and angles. It includes examples of naming these figures, classifying angles as acute, obtuse, right, complementary or supplementary. It also covers the properties that vertical angles are congruent and that angle measures on a line or circle add to 180° and 360°, respectively. The document contains examples and problems for students to practice these geometric concepts.
Lecture co1 math 21-1
1) The document outlines the course outcomes for Calculus I with Analytic Geometry. It discusses fundamental concepts like analytic geometry, functions, limits, continuity, derivatives, and their applications.
2) The course aims to teach students to analyze and solve problems involving lines, circles, conics, transcendental functions, derivatives, tangents, normals, maxima/minima, and related rates.
3) The assessment tasks and grading criteria are also presented, including quizzes, classwork, and a final examination. Minimum averages for satisfactory performance are provided.
1.1.1A Points, Lines, and Planes
This document defines and provides examples of key geometric concepts including points, lines, line segments, rays, planes, and their relationships. It defines points as having no dimensions, lines as straight paths extending indefinitely, line segments as parts of lines between two endpoints, and rays as parts of lines extending from an endpoint in one direction. Planes are defined as flat surfaces extending indefinitely. Examples are provided to demonstrate collinear points that lie on the same line, coplanar points that lie in the same plane, and basic postulates such as two points defining a single unique line. Key terms are summarized in a table for easy reference.
Coordinate geometry
Coordinate geometry
easy to learn points
class 9 cbse course ncert textbook
Quiz
Maths trivia quiz
1.1.1B Measuring Segments
Calculate the distance between two points
Set up and solve linear equations using segment addition and midpoint properties
Correctly use notation for distance and segments
GEOMETRY: POINTS, LINES. PLANES
The document discusses basic concepts in geometry including points, lines, planes, and their relationships. It defines a point as having no size or shape, a line as connecting two or more points and extending indefinitely in both directions, and a plane as a flat two-dimensional surface containing points and lines. The document provides examples of naming points, lines, and planes and identifies collinear points that lie on the same line and coplanar points that lie on the same plane. It includes practice problems asking students to name, draw, and identify various geometric concepts.
Geometry Section 1-1 1112
This document introduces key concepts in geometry including points, lines, planes, collinear points, coplanar points, and intersections. It defines points as having no size or shape, lines as infinite sets of points with no thickness, and planes as flat surfaces determined by three or more points that extend infinitely. Examples demonstrate identifying geometric objects from diagrams and real-world situations. Vocabulary and concepts are applied in problems identifying and relating points, lines and planes.
1-2 PowerPoint.pptx
This document defines basic geometry terms like point, line, and plane which are undefined terms that serve as building blocks. It also introduces defined terms like segment and ray. Postulates are accepted statements of fact in geometry, such as through any two points there is exactly one line. The document provides examples applying these terms and postulates to identify collinear points, coplanar lines, and intersecting planes.
More Related Content
What's hot
1 1 understanding points, lines, & planes
This document is from a Holt Geometry textbook and covers key concepts about points, lines, and planes. It defines points, lines, and planes as undefined terms that are building blocks of geometry. It discusses properties such as collinear points on a line, coplanar points on a plane, and intersections between lines and planes. Examples demonstrate naming and drawing points, lines, segments, rays, and planes as well as representing intersections between geometric figures.
Geometry lesson
This geometry lesson document introduces key concepts about points, lines, and planes. It defines points, lines, and planes as the basic undefined terms or building blocks of geometry. It discusses properties such as collinear points that lie on the same line, and coplanar points that lie on the same plane. The document provides examples of naming and drawing points, lines, segments, rays, and planes. It also covers basic facts about intersections of lines and planes.
Properties of Geometric Figures
This document defines key geometric terms and concepts including:
- Collinear points which lie on the same line. Coplanar points which lie on the same plane.
- Five postulates outline the fundamental properties of points, lines, and planes: any two points define a single unique line; a plane contains at least three non-collinear points; any three points lie in a single plane; intersecting lines or planes meet at a point or line.
- Theorems describe relationships between lines and planes, such as two intersecting lines lying in a single plane, or a line and point not on the line defining a unique plane.
Introduction to coordinate geometry
Any point on a plane can be named with two numbers called coordinates - an x-coordinate for the distance from the origin along the x-axis and a y-coordinate for the distance along the y-axis. The coordinate grid is divided into four quadrants by the x and y axes, and points can be plotted in the grid and identified by their coordinates and quadrant. Linear equations can be graphed by making a table of solutions and plotting the points, then drawing a straight line through them.
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeks
This document provides an introduction to mathematics concepts for direct3D game programming, including:
- 2D rotation formulas for rotating a point about an angle
- Definitions of domain, codomain, exponentiation, factorial, square root, and cubic root
- Explanations of inverse functions, Pythagorean theorem, summation notation, and practice problems for various concepts
- Overviews of the Cartesian coordinate system, trigonometric functions, and how to implement them in programs
Ac1.2gMorePracticeProblems
More practice with naming points, lines and planes and observing what is going on in diagrams. This is for high school students
Points, Lines and Planes
This document defines key geometry concepts such as points, lines, planes, and their relationships. It provides examples of naming points, lines, and planes, including collinear points that lie on the same line and coplanar points that lie in the same plane. Examples also demonstrate naming segments and rays with different endpoints, and identifying opposite rays. Diagrams show intersecting lines and planes, including lines within a plane, lines that do not intersect a plane, and lines intersecting a plane at a point. Two intersecting planes are shown meeting at a line of intersection. Guided practice problems apply the concepts to name intersections and identify relationships in diagrams.
1 2 Points, Lines, And Planes
This document defines and explains basic geometric terms and postulates. It defines a point as having no size and being represented by a dot. It defines a line as a series of points that extends in two opposite directions without end. It defines a plane as a flat surface that extends infinitely in length and width, having no thickness. It states postulates such as through any two points there is exactly one line, if two lines intersect they intersect at exactly one point, and if two planes intersect they intersect at exactly one line.
Basics Of Geometry 1
The document introduces some basic concepts in geometry, including:
1. Points, lines, and planes are undefined terms that form the foundations of geometry.
2. It explains concepts like collinear points, coplanar points, line segments, rays, and how to classify angles.
3. It discusses intersections of lines, planes, and examples of modeling intersections of geometric figures.
1.2 Ruler Postulates
The document discusses three geometric postulates:
1) The ruler postulate establishes a one-to-one correspondence between points on a line and real numbers on the number line, where the distance between points equals the absolute value of the difference of their corresponding numbers.
2) The ruler placement postulate allows choosing a number line such that two given points correspond to 0 and a positive number.
3) The segment addition postulate states that if one point is between two others, the sum of the distances to the end points equals the distance between the outer points.
GEOMETRY: POINTS, LINES. PLANE
By this end of the presentation you will be able to:
Identify and model points, lines, and planes.
Identify collinear and coplanar points.
Identify non collinear and non coplanar points.
Topic 1. points, line and plane
The three undefined terms in geometry are point, line, and plane. A point indicates a position in space and is named with capital letters or coordinates. A line is an infinite set of adjacent points that extends in both directions, named using two points or a lowercase letter. A plane is a flat surface that extends indefinitely in all directions, named using three points or an uppercase letter.
Language of Geometry
This document introduces basic geometric concepts including points, lines, and planes. It defines these terms and provides examples of representing them visually. Key points covered include:
- A point has no dimension and is represented by a dot.
- A line consists of infinitely many points and is shown as an arrowed line.
- A plane is a flat, thickness-less surface that extends indefinitely in all directions and is usually pictured as a four-sided shape.
- Coplanar and collinear points are defined in relation to lying on the same plane or line, respectively.
Math14 lesson 5
The document discusses different types of equations that can represent straight lines in a plane, including point-slope form, two-point form, slope-intercept form, and normal form. It provides examples of writing the equation of a line given characteristics like two points, slope and intercept, or being parallel/perpendicular to another line. The document also covers topics like finding the distance from a point to a line and the equations of angle bisectors.
1.2 points, lines and planes
This document provides lesson material on classifying and naming geometric figures such as points, lines, planes, segments, rays, and angles. It includes examples of naming these figures, classifying angles as acute, obtuse, right, complementary or supplementary. It also covers the properties that vertical angles are congruent and that angle measures on a line or circle add to 180° and 360°, respectively. The document contains examples and problems for students to practice these geometric concepts.
Lecture co1 math 21-1
1) The document outlines the course outcomes for Calculus I with Analytic Geometry. It discusses fundamental concepts like analytic geometry, functions, limits, continuity, derivatives, and their applications.
2) The course aims to teach students to analyze and solve problems involving lines, circles, conics, transcendental functions, derivatives, tangents, normals, maxima/minima, and related rates.
3) The assessment tasks and grading criteria are also presented, including quizzes, classwork, and a final examination. Minimum averages for satisfactory performance are provided.
1.1.1A Points, Lines, and Planes
This document defines and provides examples of key geometric concepts including points, lines, line segments, rays, planes, and their relationships. It defines points as having no dimensions, lines as straight paths extending indefinitely, line segments as parts of lines between two endpoints, and rays as parts of lines extending from an endpoint in one direction. Planes are defined as flat surfaces extending indefinitely. Examples are provided to demonstrate collinear points that lie on the same line, coplanar points that lie in the same plane, and basic postulates such as two points defining a single unique line. Key terms are summarized in a table for easy reference.
Coordinate geometry
Coordinate geometry
easy to learn points
class 9 cbse course ncert textbook
Quiz
Maths trivia quiz
1.1.1B Measuring Segments
Calculate the distance between two points
Set up and solve linear equations using segment addition and midpoint properties
Correctly use notation for distance and segments
GEOMETRY: POINTS, LINES. PLANES
The document discusses basic concepts in geometry including points, lines, planes, and their relationships. It defines a point as having no size or shape, a line as connecting two or more points and extending indefinitely in both directions, and a plane as a flat two-dimensional surface containing points and lines. The document provides examples of naming points, lines, and planes and identifies collinear points that lie on the same line and coplanar points that lie on the same plane. It includes practice problems asking students to name, draw, and identify various geometric concepts.
What's hot (20)
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeks
Beginning direct3d gameprogrammingmath01_primer_20160324_jintaeks
Similar to Gch1 l1
Geometry Section 1-1 1112
This document introduces key concepts in geometry including points, lines, planes, collinear points, coplanar points, and intersections. It defines points as having no size or shape, lines as infinite sets of points with no thickness, and planes as flat surfaces determined by three or more points that extend infinitely. Examples demonstrate identifying geometric objects from diagrams and real-world situations. Vocabulary and concepts are applied in problems identifying and relating points, lines and planes.
1-2 PowerPoint.pptx
This document defines basic geometry terms like point, line, and plane which are undefined terms that serve as building blocks. It also introduces defined terms like segment and ray. Postulates are accepted statements of fact in geometry, such as through any two points there is exactly one line. The document provides examples applying these terms and postulates to identify collinear points, coplanar lines, and intersecting planes.
Gch3 l1
This document is from a Holt Geometry textbook and covers lines and angles. It defines different types of lines such as parallel, perpendicular, and skew lines. It also defines angle pairs that are formed when two lines intersect with a third line called a transversal, such as corresponding angles, alternate interior angles, alternate exterior angles, and same-side interior angles. The document provides examples of identifying these different types of lines and classifying angles into the different pairs. It concludes with a short quiz to assess understanding.
Math8Q3Module1 .pptx
The document discusses the mathematical system in geometry. It defines key undefined terms like point, line, and plane. It explains that a geometry system needs defined terms, undefined terms, postulates, and theorems. It then covers lessons about identifying points, lines, and planes; collinear and coplanar points/lines; and postulates related to points, lines, and planes. Specifically, it outlines four postulates: 1) through any two points there is exactly one line, 2) if two lines intersect they do so at exactly one point, 3) if two planes intersect they do so at exactly one line, and 4) through any three noncollinear points there is exactly one plane.
Gch3 l6
This document provides a lesson on lines in the coordinate plane. It includes examples of writing equations of lines in slope-intercept and point-slope form, graphing lines, and classifying pairs of lines as parallel, intersecting, or coinciding. It also contains a problem-solving application example involving writing equations to represent two car rental plans and finding where the lines intersect to determine the mileage where the plans' costs are equal.
Gch1 l6
This document is from a geometry textbook and covers finding midpoints and distances on a coordinate plane. It begins with examples of using the midpoint formula to find the coordinates of midpoints and endpoints. It then introduces the Distance Formula and Pythagorean Theorem for finding distances between points. Several examples demonstrate using these concepts to solve problems involving midpoints and distances in the coordinate plane. Key terms like coordinate plane, leg, and hypotenuse are also defined.
KMAO.ppt
This document is from a Holt Geometry textbook and covers solid geometry. It defines three-dimensional figures and their components such as faces, edges, and vertices. Examples are given to classify figures by their properties and identify figures from nets. Cross sections of figures are also described. The document aims to teach students to analyze and classify three-dimensional shapes.
Geometry Section 1-1
This document introduces basic geometry concepts such as points, lines, planes, and their intersections. It defines a point as having no size or shape, a line as an infinite set of collinear points, and a plane as a flat surface extending indefinitely. Examples demonstrate identifying geometric shapes from real-world objects and graphing points and lines on a coordinate plane. The summary defines key terms and provides examples of geometric concepts and relationships.
Chapter 1-1 Review
1. The document defines key terms used in geometry such as point, line, line segment, ray, plane, and their properties. It also lists postulates about points, lines, and planes.
2. Examples are provided to demonstrate naming and drawing points, lines, segments, rays, and planes as well as identifying intersections and objects contained within a plane.
3. Readers are encouraged to study the vocabulary and practice the example problems at the end of the chapter.
10-1 Intro to Conic Sections- class.ppt
The document is a lesson on conic sections from Holt Algebra 2. It introduces the four types of conic sections - circles, ellipses, hyperbolas, and parabolas - and explains that they are formed by the intersection of a plane and a double right cone. Examples are provided on graphing each type of conic section on a calculator and identifying their characteristics like center, intercepts, vertices or direction of opening. The lesson also explains how to find the center and radius of a circle using the midpoint and distance formulas.
geometry.pptx
Geometry deals with properties and relations of lines, angles, surfaces, and solids. A point has no length, breadth or thickness and represents a position. A line extends indefinitely in both directions from a point. A plane has no boundaries and flat surfaces are plane surfaces. Three or more collinear points all lie on the same line.
lec-2 geometry1.pptx
Geometry deals with properties and relations of lines, angles, surfaces, and solids. A plane has no boundaries and flat surfaces are plane surfaces. A point is a mark of position with no length, breadth or thickness. A line segment has a definite length, while a line has no end points. A ray is a line segment extended endlessly in one direction. Intersecting lines cross and share a common point, while parallel lines remain at an equal distance and never meet. Collinear points all lie on the same line.
Chapter_11.pdf
This document discusses Boolean algebra and its fundamental concepts. It introduces Boolean algebra, which was developed by George Boole to express logical reasoning mathematically. Boolean algebra uses two values (1 and 0) and two operations (addition and multiplication). Addition represents logical OR, while multiplication represents logical AND. Logic gates like OR gates and AND gates perform Boolean operations. The document also covers de Morgan's theorems, duality, and proofs of several rules of Boolean algebra.
Coordinate geometry 9 grade
This document provides an introduction to coordinate geometry and the Cartesian coordinate system. It defines key terms like coordinates, quadrants, and plotting points. The Cartesian plane is formed by the intersection of the x and y axes, with the origin at (0,0). Any point can be uniquely identified using an ordered pair (x,y) representing the distances from the x and y axes. Examples are given of plotting points and calculating distances between points on the plane using their coordinates. In summary, the document outlines the basic concepts of the Cartesian coordinate system used in coordinate geometry.
Gch9 l4
This document contains a geometry lesson on calculating the perimeters and areas of polygons in the coordinate plane. It includes examples of estimating areas of irregular shapes using grids, finding perimeters and areas of parallelograms, and subtracting areas of additional shapes from a bounding rectangle. One example shows two composite figures that appear to have different areas but are proved to have the same area through calculation. The lesson concludes with a quiz to assess understanding of finding perimeters and areas of polygons in the coordinate plane.
Ac1.5cMorePracticeProblems
The document discusses theorems and postulates regarding lines and planes in geometry. It provides exercises asking to state theorems, name lines and planes based on given points, and determine whether certain geometric configurations are possible according to established postulates. For some exercises, it asks the reader to visualize lines and planes not shown in an accompanying diagram.
Mathematical System.pptx
The document discusses the key components of a mathematical system:
1. Undefined terms are concepts that cannot be precisely defined, such as points, lines, and planes in geometry.
2. Defined terms have a formal definition using undefined terms or other defined terms, such as line segments, rays, and collinear/coplanar points.
3. Axioms or postulates are statements assumed to be true without proof, which can be used to prove theorems.
4. Theorems are statements that have been formally proven using axioms, postulates and previously proven theorems. The four components are related such that defined terms are defined using undefined terms, axioms are
1 3 points, lines, planes
This document defines key geometric concepts including points, lines, planes and their relationships. It explains that points have no size, lines extend indefinitely and planes are flat surfaces that extend without limits. It also covers topics like collinear points that lie on the same line, determining if objects are coplanar by lying on the same plane, and the different types of intersections between lines and planes, which can be a point, line or no intersection.
R lecture co2_math 21-1
Discuss comprehensively the fundamental concepts in Analytic Geometry and use them to solve application problems and problems involving lines.
A geom ocultanasleisfisicas
This document discusses polyadic geometry, which uses polyadic calculus to represent physical laws through tensors and free polyadics of different valences. It explains that polyadics of valence zero are scalars, valence one are vectors, and higher valences (H) are H-adics like dyadics and triadics. The document outlines how polyadic spaces are conceived similarly to vector spaces, with dimensions of an H-adic space being 3H. It also describes how to construct geometric figures like pyramids in polyadic spaces and extend concepts like trigonometry and medians to higher dimensions using polyadic representations.
Similar to Gch1 l1 (20)
More from Matt Fillingham
Gch10 l8
This document discusses spheres and their volumes and surface areas. It includes examples of calculating volumes and surface areas of spheres and composite figures containing spheres. Formulas used include the volume of a sphere equaling (4/3)πr^3 and the surface area equaling 4πr^2. Examples show multiplying or dividing the radius changes the volume and surface area. The document contains warm up questions, objectives, vocabulary, lesson material and examples, and a quiz on spheres.
Gch10 l7
This document discusses calculating the volumes of pyramids, cones, and composite three-dimensional figures. It provides examples of finding volumes of different shapes, such as rectangular and square pyramids, cylinders, and cones. It also explores how changing the dimensions of these figures affects their volumes. Formulas are given for calculating the volumes of pyramids and cones based on their base areas and heights.
Gch10 l6
This document discusses calculating the volumes of prisms and cylinders. It provides examples of using the formulas for volume of a prism (V=lwh) and cylinder (V=πr^2h) to find volumes. It also explores how changing the dimensions of prisms and cylinders affects their volumes. For prisms, doubling the length, width, and height increases the volume by 8 times. For cylinders, doubling the radius and height quadruples the volume.
Gch10 l5
This document provides instruction on calculating the surface areas of pyramids and cones. It begins with key vocabulary terms like vertex, slant height, and altitude. Examples are then given of using the surface area formulas to find the lateral and total surface areas of regular pyramids and right cones when given dimensions like base length and slant height. The effects of changing dimensions on surface area are explored, and a manufacturing application involving cones is presented.
Gch10 l4
This document provides instruction on calculating the surface areas of prisms and cylinders. It includes definitions of key terms like lateral face and altitude. Formulas are provided for calculating the surface area of a right rectangular prism and a right cylinder. Examples show how to use the formulas to find the surface area of various prisms and cylinders. Effects of changing dimensions on surface area are also explored through examples.
Gch10 l1
This document is from a Holt Geometry textbook and covers solid geometry. It defines three-dimensional figures like prisms, pyramids, cylinders and cones. It discusses how to classify solids based on their vertices, edges and bases. It also covers nets, which are diagrams that can be folded to form three-dimensional figures, and cross sections, which are shapes revealed when a solid is cut by a plane. Examples are provided to identify solids from nets and describe cross sections. Food applications involving cutting cheese and watermelon are also discussed.
Gch8 l4
This document is from a Holt Geometry textbook and covers angles of elevation and depression. It includes examples of classifying angles as elevation or depression, using tangent ratios to find distances given an elevation or depression angle, and multi-step word problems combining these concepts. Warm-up questions, vocabulary, lesson objectives, examples with step-by-step solutions, and a lesson quiz are provided.
Gch8 l3
This document discusses solving right triangles using trigonometric ratios. It includes examples of identifying angles from trigonometric ratios, calculating angle measures from ratios using inverse functions, solving right triangles when given side lengths or an angle measure, and solving triangles in the coordinate plane. One example problem solves for the angle of a road given its grade in percentage form.
Gch8 l2
This document discusses trigonometric ratios and their use in solving problems involving right triangles. It begins with examples of writing trigonometric ratios (sine, cosine, tangent) as fractions and decimals for given angles. It then demonstrates using trigonometric ratios to find side lengths in right triangles when one or two sides and the angle between them is known. Several examples are provided to illustrate finding unknown side lengths by setting up and solving equations based on the appropriate trigonometric ratio. The document concludes with an example of applying trigonometric ratios to solve a real-world problem involving finding the length of an inclined railway track given the rise and angle of inclination.
Gch5 l8
This document is from a Holt Geometry textbook and covers applying special right triangles. It includes examples of using 45-45-90 and 30-60-90 triangles to find unknown side lengths. Key relationships covered are that for a 45-45-90 triangle the hypotenuse is √2 times the leg and for a 30-60-90 triangle the hypotenuse is 2 times the shorter leg. Examples include finding side lengths, checking solutions, and solving applied problems involving diagonal lengths of squares and equilateral triangles. The lesson ends with a quiz to test understanding of using these special right triangle relationships.
Gch5 l7
This document is a lesson on the Pythagorean theorem from a Holt Geometry textbook. It begins with examples of using the Pythagorean theorem to solve for missing sides of right triangles. It then discusses how to identify if a set of three sides forms a Pythagorean triple. The lesson continues with examples of using the converse of the Pythagorean theorem and Pythagorean inequalities to classify triangles as right, acute, or obtuse based on their side lengths. It concludes with a two-part lesson quiz reviewing the material.
Gch5 l6
This document discusses using inequalities to compare angles and side lengths in two triangles. It begins with examples that use the hinge theorem and its converse to determine relationships between angles and sides. Application examples are provided, including comparing distances traveled from school. Proofs are presented to demonstrate triangle relationships using statements and reasons. The document concludes with a lesson quiz to assess understanding.
Gch5 l5
This document provides a lesson on indirect proofs and inequalities in one triangle from Holt Geometry. It includes examples of writing indirect proofs, ordering triangle side lengths and angle measures, applying the triangle inequality theorem, finding possible side lengths of a triangle, and using triangle inequalities in a travel application problem. Practice problems are provided to check understanding. The key concepts covered are indirect proof, triangle inequalities, and relating triangle side lengths to angle measures.
Gch04 l8
This document discusses properties of isosceles and equilateral triangles. It begins with examples calculating angle measures using properties of isosceles triangles, such as the fact that the two base angles of an isosceles triangle are congruent. It then proves theorems about isosceles and equilateral triangles, including that an equilateral triangle is also equiangular. Coordinate proofs are presented to show properties such as the midpoint of the two sides of an isosceles triangle bisecting the base. The document concludes with a lesson quiz reviewing the material.
Gch04 l5
This document discusses different methods for proving triangles congruent:
- ASA (Angle-Side-Angle) congruence can be used if two angles and the included side are congruent.
- AAS (Angle-Angle-Side) congruence can be used if two angles of one triangle are congruent to two angles of another triangle and one side included between the angles is congruent.
- HL (Hypotenuse-Leg) congruence can be used if two right triangles have one leg and the hypotenuse congruent.
Examples are provided to demonstrate applications of each method of triangle congruence.
Gch04 l4
This document discusses triangle congruence using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It provides examples of using SSS and SAS to prove that two triangles are congruent. Key concepts covered include triangle rigidity, included angles, and applying SSS and SAS to solve problems and construct congruent triangles. Worked examples demonstrate using SSS and SAS, along with step-by-step proofs of triangle congruence.
Gch04 l3
The document is from a geometry textbook and covers congruent triangles. It defines congruent triangles as those that are the same size and shape, with corresponding angles and sides being equal. Examples are provided of naming corresponding parts of congruent triangles and using properties of congruent triangles to prove other triangles are congruent or find missing angle measures. An engineering application example proves two triangles congruent based on bisecting lines and equal corresponding parts.
Gch04 l2
This document is from a geometry textbook and covers angle relationships in triangles. It begins with examples of finding missing angle measures using the Triangle Sum Theorem, Linear Pair Theorem, and exterior angle theorem. It then discusses properties of interior and exterior angles and applying the Third Angle Theorem. The document includes examples, practice problems, and key vocabulary terms like interior, exterior, and remote interior angles. It provides instruction and practice for finding missing angle measures in different types of triangles.
Gch04 l1
This document provides a lesson on classifying triangles based on their angle measures and side lengths. Triangles can be classified as acute, obtuse, right, equiangular, equilateral, isosceles or scalene. Examples show how to determine the type of triangle based on the given information. The lesson concludes with examples of applying triangle classification to find missing side lengths or determine how many triangles can be made from a given amount of material.
Gch6 l2
This document discusses properties of parallelograms from a geometry textbook. It includes examples of using properties such as opposite sides being equal, opposite angles being equal, and diagonals bisecting each other to solve problems about parallelograms. It also covers using parallelogram properties to write two-column proofs and finding coordinates of the fourth vertex of a parallelogram given three vertices.
More from Matt Fillingham (20)
Recently uploaded
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience Wahiba Chair Training & Consulting
Wahiba Chair's Talk at the 2024 Learning Ideas Conference. BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdবাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneAdvanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Recently uploaded (20)
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Gch1 l1
- 1. Holt Geometry 1-1 Understanding Points, Lines, and Planes1-1 Understanding Points, Lines, and Planes Holt Geometry Warm UpWarm Up Lesson PresentationLesson Presentation Lesson QuizLesson Quiz
- 2. Holt Geometry 1-1 Understanding Points, Lines, and Planes Warm Up Graph each inequality. 1. x ≥ 3 2. 2 ≤ x ≤ 6 3. x < 1 OR x > 0 -2 0 2 4 0 2 4 6 0 1
- 3. Holt Geometry 1-1 Understanding Points, Lines, and Planes Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes. Objectives
- 4. Holt Geometry 1-1 Understanding Points, Lines, and Planes undefined term point line plane collinear coplanar segment endpoint ray opposite rays postulate Vocabulary
- 5. Holt Geometry 1-1 Understanding Points, Lines, and Planes The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.
- 6. Holt Geometry 1-1 Understanding Points, Lines, and Planes
- 7. Holt Geometry 1-1 Understanding Points, Lines, and Planes Points that lie on the same line are collinear. K, L, and M are collinear. K, L, and N are noncollinear. Points that lie on the same plane are coplanar. Otherwise they are noncoplanar. M K L N
- 8. Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 1: Naming Points, Lines, and Planes A. Name four coplanar points. B. Name three lines. A, B, C, D Possible answer: AE, BE, CE
- 9. Holt Geometry 1-1 Understanding Points, Lines, and Planes Use the diagram to name two planes. Check It Out! Example 1 Possible answer: Plane R and plane ABC.
- 10. Holt Geometry 1-1 Understanding Points, Lines, and Planes
- 11. Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 2: Drawing Segments and Rays Draw and label each of the following. A. a segment with endpoints M and N. B. opposite rays with a common endpoint T. M N T
- 12. Holt Geometry 1-1 Understanding Points, Lines, and Planes Draw and label a ray with endpoint M that contains N. Check It Out! Example 2 M N
- 13. Holt Geometry 1-1 Understanding Points, Lines, and Planes A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.
- 14. Holt Geometry 1-1 Understanding Points, Lines, and Planes
- 15. Holt Geometry 1-1 Understanding Points, Lines, and Planes Name a line that passes through two points. Example 3: Identifying Points and Lines in a Plane XY
- 16. Holt Geometry 1-1 Understanding Points, Lines, and Planes Name a plane that contains three noncollinear points. Check It Out! Example 3 Possible answer: plane GHF
- 17. Holt Geometry 1-1 Understanding Points, Lines, and Planes Recall that a system of equations is a set of two or more equations containing two or more of the same variables. The coordinates of the solution of the system satisfy all equations in the system. These coordinates also locate the point where all the graphs of the equations in the system intersect. An intersection is the set of all points that two or more figures have in common. The next two postulates describe intersections involving lines and planes.
- 18. Holt Geometry 1-1 Understanding Points, Lines, and Planes
- 19. Holt Geometry 1-1 Understanding Points, Lines, and Planes Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.
- 20. Holt Geometry 1-1 Understanding Points, Lines, and Planes Example 4: Representing Intersections A. Sketch two lines intersecting in exactly one point. B. Sketch a figure that shows a line that lies in a plane.
- 21. Holt Geometry 1-1 Understanding Points, Lines, and Planes Check It Out! Example 4 Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.
- 22. Holt Geometry 1-1 Understanding Points, Lines, and Planes Lesson Quiz: Part I 1. Two opposite rays. 3. The intersection of plane N and plane T. 4. A plane containing E, D, and B. 2. A point on BC. CB and CD Possible answer: D Possible answer: BD Plane T
- 23. Holt Geometry 1-1 Understanding Points, Lines, and Planes Lesson Quiz: Part II 5. a line intersecting a plane at one point 6. a ray with endpoint P that passes through Q Draw each of the following.