1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg.
2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex.
3. Lines are then drawn between the vertices to complete the triangle.
The document defines and discusses congruence of geometric shapes. It states that two shapes are congruent if one can be transformed into the other using turns, flips, or slides. It then discusses congruence as it relates to lines, angles, vertices, triangles (scalene, isosceles, equilateral), quadrilaterals, and circles. Specifically, it notes that line segments of equal length and angles of equal measure are congruent, and provides examples of congruent triangles and quadrilaterals based on matching sides and angles.
The document defines and discusses different types of polygons. The main points are:
1. A polygon is a plane figure formed by three or more line segments that intersect only at their endpoints to form a closed region.
2. Polygons can be classified as convex or concave based on whether any line segment connecting two points within the polygon lies entirely inside or outside the polygon.
3. Regular polygons are polygons that are both equilateral (all sides the same length) and equiangular (all interior angles the same measure).
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7Gilbert Joseph Abueg
The document discusses angles and parallel lines. It defines parallel lines and transversals, and explains that when a transversal intersects parallel lines, it forms eight angles that can be classified as vertical, corresponding, alternate interior, alternate exterior, adjacent, consecutive interior, and consecutive exterior angles. The document states that if two parallel lines are cut by a transversal, vertical angles, corresponding angles, alternate interior angles, and alternate exterior angles are congruent, while adjacent angles, consecutive interior angles, and consecutive exterior angles are supplementary. An example problem demonstrates finding angle measures given one is known.
The document provides examples of various geometric shapes found in architecture around the world and defines each shape. It begins by using the Capital Building to represent a point and the Empire State Building to represent a line segment. It then discusses planes, angles, perpendicular and parallel lines using various buildings as examples. The summary concludes with triangles, right triangles, polygons up to hexagons, and three-dimensional shapes including cubes, cylinders, spheres, and polyhedrons being represented by different architectural structures.
This document defines and compares different types of quadrilaterals, focusing on parallelograms. It describes the key properties of parallelograms, rectangles, rhombuses, squares, kites, isosceles trapezoids, including their definitions, angles, sides, and diagonal properties. Diagrams illustrate each shape. The document also shows the relationships between these special quadrilaterals and parallelograms.
The document discusses different geometric properties of triangles including medians, centroids, and altitudes. A median is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle intersect at the centroid, which divides each median into segments with a ratio of 2:1. An altitude is a segment drawn from a vertex perpendicular to the opposite side, and can be inside, on, or outside the triangle depending on if the triangle is acute, right, or obtuse.
Parallel Lines Cut by a Transversal PPT 1-9-2018.pptxRayRabara
This document discusses parallel lines and transversals. It defines key terms like parallel lines, transversals, interior angles, and exterior angles. It explains special relationships between angles formed by parallel lines and transversals, including corresponding angles being congruent, alternate interior angles and exterior angles being congruent, and same side interior/exterior angles being supplementary. Examples and practice problems are provided to illustrate these concepts.
1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg.
2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex.
3. Lines are then drawn between the vertices to complete the triangle.
The document defines and discusses congruence of geometric shapes. It states that two shapes are congruent if one can be transformed into the other using turns, flips, or slides. It then discusses congruence as it relates to lines, angles, vertices, triangles (scalene, isosceles, equilateral), quadrilaterals, and circles. Specifically, it notes that line segments of equal length and angles of equal measure are congruent, and provides examples of congruent triangles and quadrilaterals based on matching sides and angles.
The document defines and discusses different types of polygons. The main points are:
1. A polygon is a plane figure formed by three or more line segments that intersect only at their endpoints to form a closed region.
2. Polygons can be classified as convex or concave based on whether any line segment connecting two points within the polygon lies entirely inside or outside the polygon.
3. Regular polygons are polygons that are both equilateral (all sides the same length) and equiangular (all interior angles the same measure).
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7Gilbert Joseph Abueg
The document discusses angles and parallel lines. It defines parallel lines and transversals, and explains that when a transversal intersects parallel lines, it forms eight angles that can be classified as vertical, corresponding, alternate interior, alternate exterior, adjacent, consecutive interior, and consecutive exterior angles. The document states that if two parallel lines are cut by a transversal, vertical angles, corresponding angles, alternate interior angles, and alternate exterior angles are congruent, while adjacent angles, consecutive interior angles, and consecutive exterior angles are supplementary. An example problem demonstrates finding angle measures given one is known.
The document provides examples of various geometric shapes found in architecture around the world and defines each shape. It begins by using the Capital Building to represent a point and the Empire State Building to represent a line segment. It then discusses planes, angles, perpendicular and parallel lines using various buildings as examples. The summary concludes with triangles, right triangles, polygons up to hexagons, and three-dimensional shapes including cubes, cylinders, spheres, and polyhedrons being represented by different architectural structures.
This document defines and compares different types of quadrilaterals, focusing on parallelograms. It describes the key properties of parallelograms, rectangles, rhombuses, squares, kites, isosceles trapezoids, including their definitions, angles, sides, and diagonal properties. Diagrams illustrate each shape. The document also shows the relationships between these special quadrilaterals and parallelograms.
The document discusses different geometric properties of triangles including medians, centroids, and altitudes. A median is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle intersect at the centroid, which divides each median into segments with a ratio of 2:1. An altitude is a segment drawn from a vertex perpendicular to the opposite side, and can be inside, on, or outside the triangle depending on if the triangle is acute, right, or obtuse.
Parallel Lines Cut by a Transversal PPT 1-9-2018.pptxRayRabara
This document discusses parallel lines and transversals. It defines key terms like parallel lines, transversals, interior angles, and exterior angles. It explains special relationships between angles formed by parallel lines and transversals, including corresponding angles being congruent, alternate interior angles and exterior angles being congruent, and same side interior/exterior angles being supplementary. Examples and practice problems are provided to illustrate these concepts.
The document discusses the Pythagorean theorem. It defines the terms leg and hypotenuse in a right triangle. The Pythagorean theorem states that the sum of the squares of the legs equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to solve for missing lengths in right triangles.
This document presents information about quadrilaterals and parallelograms. It defines a quadrilateral as a plane figure bounded by four line segments and lists the types of quadrilaterals - parallelogram, rectangle, square, and trapezium. Theorems about the properties of parallelograms are presented, such as opposite sides being equal and opposite angles being equal. Converses of these theorems are also discussed. Additional theorems relate to the diagonals of rectangles, rhombi, and squares. The intercept theorem states that if three lines have equal intercepts on one transversal, the intercepts will be equal on any other transversal.
This document defines and describes different types of lines and angles. It explains that lines can be rays, segments, parallel, or perpendicular and defines each type. Lines extend in opposite directions and are made up of points. The document also defines right, obtuse, and acute angles and explains their degree measurements. It includes questions to check the reader's understanding of lines and angles.
Points, lines, and planes are the basic building blocks of geometry. A point is a location without shape and is represented by a capital letter. A line contains points and has no thickness, with exactly one line passing through any two points. The intersection of two lines is a point. A plane is a flat surface made up of points that extends infinitely in all directions, with the intersection of two planes being a line. Planes are identified by a capital italicized letter or by three non-collinear points.
The document discusses different types of shapes including 2D and 3D shapes. It defines what a shape is and provides examples of 2D shapes like circles and triangles. It also defines 3D shapes as solid objects that have length, breadth and height. Examples provided include cubes and spheres. The document also discusses properties of 2D and 3D shapes such as faces, edges and vertices. Maps are also summarized as representations of locations that use symbols, colors and scales.
Quadrilateral that are parallelogram.pptxRizaCatli2
The document discusses quadrilaterals and parallelograms. It provides examples of different types of quadrilaterals like trapezoids, parallelograms, rhombuses, squares, and kites. It asks students to identify quadrilaterals and parallelograms in different shapes. It also discusses the properties of parallelograms and provides activities for students to practice identifying and classifying quadrilaterals.
The document discusses different types of polygons and their properties. It defines concave and convex polygons, interior and exterior angles, and provides a formula to calculate the sum of interior angles based on the number of sides. It also discusses regular polygons and how the sum of exterior angles is always 360 degrees for convex polygons.
This document discusses different types of graphs used to represent data. It outlines eight main types of graphs: bar graphs, pie charts, tally charts, area graphs, pictographs, waterfall graphs, line graphs, and polar graphs. Each graph type is briefly described, including details about bar graphs having two axes (X and Y), pie charts showing proportional sectors, and waterfall charts representing cumulative positive or negative values. Pictographs use pictures to represent data, while line graphs connect data points with straight lines. The document provides a high-level overview of common graph types used for data visualization.
Geometry is the branch of mathematics that studies shapes, their properties, and spatial relationships. It involves key concepts like points, lines, planes, angles, triangles, quadrilaterals, and circles. A point has no size, a line extends indefinitely, parallel lines never intersect, an angle is formed by two rays from a common point, and shapes like triangles and quadrilaterals are classified by their properties. The document provides definitions and examples of basic geometric terms.
Pythagoras' Theorem allows you to calculate the lengths of sides in a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be used to find missing side lengths or to determine if a triangle is right-angled. It is commonly applied to problems involving distances, lengths, and geometrical shapes containing right triangles.
The document defines and compares different types of quadrilaterals. A quadrilateral is a closed shape with four sides whose interior angles sum to 360 degrees. The main quadrilaterals discussed are: parallelograms, which have opposite sides that are parallel and equal; rectangles, which have four right angles; rhombi, which have four equal sides; squares, which are rhombi with four right angles; kites, which have two pairs of equal sides that meet at a right angle; and trapezoids, which have one set of parallel sides. Key differences between kites, squares, rhombi and parallelograms are outlined.
Angles formed by parallel lines cut by transversalMay Bundang
If parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent. Interior angles and exterior angles on the same side of the transversal are supplementary. The document provides examples of angle measurements that illustrate these properties and includes practice problems asking to determine angle measures using these relationships.
This document introduces polygons and provides examples of different types of polygons. It defines a polygon as a two-dimensional, closed figure made up of three or more straight line segments that meet at vertices. Common polygons include triangles, quadrilaterals, pentagons, hexagons, and others up to dodecagons. Each polygon type has a specific number of sides and various sub-types are described.
Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.
This document discusses different types of triangles, including isosceles triangles, equilateral triangles, and using properties of these triangles to solve problems. It defines key parts of isosceles triangles, states properties such as the angle bisector theorem and converse isosceles triangle theorem, and provides examples of solving for missing angle and side measures in various triangles.
This document defines and provides examples of basic geometric terms including:
- Points have no dimensions and define an exact location in space.
- Lines extend infinitely in both directions and have no beginning or end.
- Angles are formed by two rays with a common endpoint and are measured in degrees. Common angles include acute, right, obtuse, and straight angles.
- Plane figures like circles, polygons, and quadrilaterals are two-dimensional shapes on a flat surface.
- Solid figures have depth and include spheres, cones, cylinders, pyramids, prisms, and cubes. They are defined by their faces, edges, vertices, and sometimes a base.
The document discusses various properties and theorems related to triangles. It begins by defining different types of triangles based on side lengths and angle measures. It then covers the four congruence rules for triangles: SAS, ASA, AAS, and SSS. The document proceeds to prove several theorems about relationships between sides and angles of triangles, such as opposite sides/angles of isosceles triangles being equal, larger sides having greater opposite angles, and the sum of any two angles being greater than the third side. It concludes by proving that the perpendicular from a point to a line is the shortest segment.
The document discusses trigonometric ratios and their properties. It defines the three basic trigonometric ratios - sine, cosine, and tangent - for any angle. It also discusses reciprocal ratios like cosecant, secant, and cotangent, which are the reciprocals of the basic ratios. The document provides examples of calculating trigonometric ratios for various angles and triangles. It also examines ratios of complementary and special angles like 0, 30, 45, 60, 90 degrees.
This document discusses classifying and identifying different types of angles:
- It defines angles and describes four ways to name angles: using the vertex, number, or points with the vertex in the middle.
- It classifies angles as acute (<90°), right (90°), obtuse (>90°), or straight (180°) and provides examples of each.
- It explains that adjacent angles are side-by-side and share a vertex and ray, while vertical angles are opposite and congruent. Finding missing angle measures can use properties of vertical angles.
The document discusses various ways in which geometry is used in daily life, such as the angles in stairs, clothing hangers, and ceiling fans, as well as how geometry allows objects to be thrown maximum distances and provides location concepts. Specific examples are also given of how geometry is applied to racing bike design for efficiency and in architectural structures to withstand forces of nature. Nature itself demonstrates geometric shapes that can be seen in leaves, lunar eclipses, and other natural phenomena.
Geometry is a branch of mathematics concerned with measuring and studying the properties and relationships of points, lines, angles, surfaces and solids. It has many practical applications in areas like carpentry, painting, gardening, construction and more. Geometry is also used in many occupations including mechanical engineering, surveying, mathematics, astronomy, graphic design and computer imaging.
The document discusses the Pythagorean theorem. It defines the terms leg and hypotenuse in a right triangle. The Pythagorean theorem states that the sum of the squares of the legs equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to solve for missing lengths in right triangles.
This document presents information about quadrilaterals and parallelograms. It defines a quadrilateral as a plane figure bounded by four line segments and lists the types of quadrilaterals - parallelogram, rectangle, square, and trapezium. Theorems about the properties of parallelograms are presented, such as opposite sides being equal and opposite angles being equal. Converses of these theorems are also discussed. Additional theorems relate to the diagonals of rectangles, rhombi, and squares. The intercept theorem states that if three lines have equal intercepts on one transversal, the intercepts will be equal on any other transversal.
This document defines and describes different types of lines and angles. It explains that lines can be rays, segments, parallel, or perpendicular and defines each type. Lines extend in opposite directions and are made up of points. The document also defines right, obtuse, and acute angles and explains their degree measurements. It includes questions to check the reader's understanding of lines and angles.
Points, lines, and planes are the basic building blocks of geometry. A point is a location without shape and is represented by a capital letter. A line contains points and has no thickness, with exactly one line passing through any two points. The intersection of two lines is a point. A plane is a flat surface made up of points that extends infinitely in all directions, with the intersection of two planes being a line. Planes are identified by a capital italicized letter or by three non-collinear points.
The document discusses different types of shapes including 2D and 3D shapes. It defines what a shape is and provides examples of 2D shapes like circles and triangles. It also defines 3D shapes as solid objects that have length, breadth and height. Examples provided include cubes and spheres. The document also discusses properties of 2D and 3D shapes such as faces, edges and vertices. Maps are also summarized as representations of locations that use symbols, colors and scales.
Quadrilateral that are parallelogram.pptxRizaCatli2
The document discusses quadrilaterals and parallelograms. It provides examples of different types of quadrilaterals like trapezoids, parallelograms, rhombuses, squares, and kites. It asks students to identify quadrilaterals and parallelograms in different shapes. It also discusses the properties of parallelograms and provides activities for students to practice identifying and classifying quadrilaterals.
The document discusses different types of polygons and their properties. It defines concave and convex polygons, interior and exterior angles, and provides a formula to calculate the sum of interior angles based on the number of sides. It also discusses regular polygons and how the sum of exterior angles is always 360 degrees for convex polygons.
This document discusses different types of graphs used to represent data. It outlines eight main types of graphs: bar graphs, pie charts, tally charts, area graphs, pictographs, waterfall graphs, line graphs, and polar graphs. Each graph type is briefly described, including details about bar graphs having two axes (X and Y), pie charts showing proportional sectors, and waterfall charts representing cumulative positive or negative values. Pictographs use pictures to represent data, while line graphs connect data points with straight lines. The document provides a high-level overview of common graph types used for data visualization.
Geometry is the branch of mathematics that studies shapes, their properties, and spatial relationships. It involves key concepts like points, lines, planes, angles, triangles, quadrilaterals, and circles. A point has no size, a line extends indefinitely, parallel lines never intersect, an angle is formed by two rays from a common point, and shapes like triangles and quadrilaterals are classified by their properties. The document provides definitions and examples of basic geometric terms.
Pythagoras' Theorem allows you to calculate the lengths of sides in a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be used to find missing side lengths or to determine if a triangle is right-angled. It is commonly applied to problems involving distances, lengths, and geometrical shapes containing right triangles.
The document defines and compares different types of quadrilaterals. A quadrilateral is a closed shape with four sides whose interior angles sum to 360 degrees. The main quadrilaterals discussed are: parallelograms, which have opposite sides that are parallel and equal; rectangles, which have four right angles; rhombi, which have four equal sides; squares, which are rhombi with four right angles; kites, which have two pairs of equal sides that meet at a right angle; and trapezoids, which have one set of parallel sides. Key differences between kites, squares, rhombi and parallelograms are outlined.
Angles formed by parallel lines cut by transversalMay Bundang
If parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent. Interior angles and exterior angles on the same side of the transversal are supplementary. The document provides examples of angle measurements that illustrate these properties and includes practice problems asking to determine angle measures using these relationships.
This document introduces polygons and provides examples of different types of polygons. It defines a polygon as a two-dimensional, closed figure made up of three or more straight line segments that meet at vertices. Common polygons include triangles, quadrilaterals, pentagons, hexagons, and others up to dodecagons. Each polygon type has a specific number of sides and various sub-types are described.
Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.
This document discusses different types of triangles, including isosceles triangles, equilateral triangles, and using properties of these triangles to solve problems. It defines key parts of isosceles triangles, states properties such as the angle bisector theorem and converse isosceles triangle theorem, and provides examples of solving for missing angle and side measures in various triangles.
This document defines and provides examples of basic geometric terms including:
- Points have no dimensions and define an exact location in space.
- Lines extend infinitely in both directions and have no beginning or end.
- Angles are formed by two rays with a common endpoint and are measured in degrees. Common angles include acute, right, obtuse, and straight angles.
- Plane figures like circles, polygons, and quadrilaterals are two-dimensional shapes on a flat surface.
- Solid figures have depth and include spheres, cones, cylinders, pyramids, prisms, and cubes. They are defined by their faces, edges, vertices, and sometimes a base.
The document discusses various properties and theorems related to triangles. It begins by defining different types of triangles based on side lengths and angle measures. It then covers the four congruence rules for triangles: SAS, ASA, AAS, and SSS. The document proceeds to prove several theorems about relationships between sides and angles of triangles, such as opposite sides/angles of isosceles triangles being equal, larger sides having greater opposite angles, and the sum of any two angles being greater than the third side. It concludes by proving that the perpendicular from a point to a line is the shortest segment.
The document discusses trigonometric ratios and their properties. It defines the three basic trigonometric ratios - sine, cosine, and tangent - for any angle. It also discusses reciprocal ratios like cosecant, secant, and cotangent, which are the reciprocals of the basic ratios. The document provides examples of calculating trigonometric ratios for various angles and triangles. It also examines ratios of complementary and special angles like 0, 30, 45, 60, 90 degrees.
This document discusses classifying and identifying different types of angles:
- It defines angles and describes four ways to name angles: using the vertex, number, or points with the vertex in the middle.
- It classifies angles as acute (<90°), right (90°), obtuse (>90°), or straight (180°) and provides examples of each.
- It explains that adjacent angles are side-by-side and share a vertex and ray, while vertical angles are opposite and congruent. Finding missing angle measures can use properties of vertical angles.
The document discusses various ways in which geometry is used in daily life, such as the angles in stairs, clothing hangers, and ceiling fans, as well as how geometry allows objects to be thrown maximum distances and provides location concepts. Specific examples are also given of how geometry is applied to racing bike design for efficiency and in architectural structures to withstand forces of nature. Nature itself demonstrates geometric shapes that can be seen in leaves, lunar eclipses, and other natural phenomena.
Geometry is a branch of mathematics concerned with measuring and studying the properties and relationships of points, lines, angles, surfaces and solids. It has many practical applications in areas like carpentry, painting, gardening, construction and more. Geometry is also used in many occupations including mechanical engineering, surveying, mathematics, astronomy, graphic design and computer imaging.
Trigonometry is the branch of mathematics dealing with relationships between sides and angles of triangles. The document traces the origins of common trigonometric functions like sine, cosine, and tangent from ancient Indian and Greek mathematicians. It then explains how trigonometric ratios are used to calculate the angle of elevation of a room by measuring the wall length and diagonal distance and applying the sine ratio formula.
This document provides an overview of geometry and how it is used. It acknowledges sources and indicates this presentation is for student benefit only. Geometry studies size, shape, and spatial relationships. It is used in computer graphics, engineering, robotics, medical imaging, and other fields. Examples of geometric structures in buildings like wigwams, skyscrapers, and cars are presented. Symmetry is also discussed as an important geometric concept seen in nature and science.
The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles used for practical applications like surveying, construction, and astronomy. Some of the earliest known texts include the Egyptian Rhind Papyrus from 2000-1800 BC and the Moscow Papyrus from around 1890 BC, as well as Babylonian clay tablets such as Plimpton 322 from around 1900 BC. For example, the Moscow Papyrus contains a formula for calculating the volume of a truncated pyramid.
The document discusses various geometry concepts including angles, polygons, triangles, quadrilaterals, parallel lines, area, and volume. It defines types of angles and angle relationships formed by parallel lines. It also defines properties of triangles, quadrilaterals like parallelograms, trapezoids, and polygons. It provides formulas to calculate the area of various shapes and the circumference and volume of circles.
This document discusses different types of models used in computer science and engineering. It defines models as representations and abstractions of real or proposed systems. Models are classified as mathematical, physical, static, dynamic, linear, nonlinear, stable, unstable, analytical, numerical, descriptive, and prescriptive. Examples are provided for each type to illustrate the distinctions between mathematical, physical, static, dynamic, linear, nonlinear, stable, unstable, analytical, numerical, descriptive, and prescriptive models. Distributed-lag and autoregressive models are also introduced as special cases of regression models.
System simulation & modeling notes[sjbit]qwerty626
The document discusses simulation modeling and provides an introduction to the topic. It defines simulation as imitating the operation of a real-world process over time. Simulation models take the form of assumptions expressed mathematically or logically about the relationships between system entities. Simulation is appropriate when a system is too complex to understand through other means or to experiment with system changes safely. The document outlines the components of a system and types of models. It also describes the basic steps involved in a simulation study from problem formulation to implementation.
This document defines and describes various geometric shapes and their properties, including:
- Points, lines, line segments, rays, planes, and their relationships
- Angle types such as acute, obtuse, right, complementary, and supplementary
- Properties of triangles like sides, angles, and area calculation
- Quadrilateral types including rectangles, squares, parallelograms, trapezoids, and their area formulas
- Circle elements such as chords, diameters, radii, sectors, circumference, and area
- Polygons with defined numbers of sides such as hexagons and octagons.
The document discusses geometric modeling which is the foundation of computer-aided design (CAD). It describes the different types of geometric models including graphical models, curve models, surface models, and solid models. Graphical models include wireframe models and can be graphically deficient. Curve models must satisfy boundary conditions at start and end points. When curves are joined, they can have C0, C1 or C2 continuity depending on matching of points, tangents or curvature. The document provides examples of each type of continuity for composite curves.
This document discusses how geometry is used in daily life and provides examples. It begins by defining basic geometric concepts like segments, congruent angles/shapes, midpoints, perpendicular lines, and obtuse angles. It then gives examples of how geometry is used in fields like computer graphics, computer-aided design, robotics, medical imaging, structural engineering, protein modeling, and physics/chemistry. Specific applications and images are provided. It concludes by highlighting how geometric shapes are used to construct man-made structures from buildings to vehicles.
The document discusses different 2D geometric shapes including circles, triangles, squares, and rectangles. It provides examples of objects that represent each shape, such as a pizza being circular, a yield sign being triangular, and a photo frame being square. It also notes that shapes can be identified by counting their sides. The document contains repetitive descriptions of shapes and examples throughout.
This document discusses statistical analysis techniques including measures of central tendency, variance, standard deviation, t-tests, and levels of significance. It provides an example of using these techniques to analyze plant height data from a fertilizer experiment and determine if differences in heights between treated and untreated plants are statistically significant. The document introduces the concepts and calculations involved in describing and analyzing quantitative data using common statistical methods.
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, polygons, circles, cylinders, spheres, and various types of triangles. It provides definitions for point, line, plane, angle, perpendicular and parallel lines, triangles, right triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, acute triangles, obtuse angles, and octagons.
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other polygons. It provides definitions for fundamental geometric objects and their characteristics in only a sentence or two per term to concisely outline key concepts in geometry.
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other polygons. Key geometric concepts covered are undefined terms, lines and their components, angles, perpendicular and parallel lines, properties of triangles, quadrilaterals, circles, cylinders, spheres, and other common polygons.
The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, and spheres. Key properties are outlined such as a point having no size, a line extending indefinitely, angles formed by rays, types of triangles based on angle measures, and properties of quadrilaterals like squares, rectangles, trapezoids, and parallelograms.
This document defines and describes basic geometric shapes and terms. It explains that a point has no size, a line has two points and all points in between, and a plane is a flat surface that extends infinitely. It then defines angles, perpendicular and parallel lines, triangles, right triangles, polygons from 3 to 12 sides, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, arcs, and cones.
This geometry project presentation covers various geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and pyramids. Key geometric concepts that will be discussed are undefined terms in geometry, different types of lines and their properties, various polygons defined by their number of sides, as well as circles, cylinders, spheres, and how triangles are classified by their angle measures.
This document defines and describes basic geometric shapes including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, cones, and polygons. Points have no size, lines extend forever and have no thickness, planes extend forever and have no thickness. Angles are formed by two rays with a common endpoint. Triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, rhombuses, and octagons are defined as polygons with a certain number of sides and properties. Circles are sets of points equidistant from the center, cylinders have two circular bases, spheres are sets of points equidistant from the center, and con
The document defines and describes basic geometric shapes and terms. It explains what a point, line segment, plane, angle, perpendicular and parallel lines, triangles, right triangles, polygons, circles, cylinders, spheres, and other shapes are. It also defines edge and angle bisector.
The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cylinders, cones, prisms and more. It provides the key properties of each shape such as the number of sides, angles, parallel or perpendicular lines, and other distinguishing characteristics.
This document defines and describes various geometric shapes and figures:
1) It defines basic shapes like points, lines, planes, angles, and perpendicular and parallel lines.
2) It also defines polygons like triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, and octagons.
3) More complex 3D shapes are also defined, such as circles, cylinders, spheres, triangular prisms, and rectangular pyramids.
The document defines and describes various geometric shapes used in golf, including points, line segments, planes, angles, triangles, squares, circles, spheres, cubes and more. It provides the basic definitions and properties of each shape, such as a point being a location in space, a line segment being bounded by two endpoints, a triangle consisting of three line segments linked end to end, a circle forming a closed loop with all points a fixed distance from the center, and a sphere having all points equidistant from its center.
Geometry in the Real World Project (Mrs. Sykes)ARitz11
The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cylinders, cones, and pyramids. It provides definitions for common shapes such as squares, rectangles, trapezoids, and parallelograms. It also introduces polygons with specific numbers of sides such as triangles, pentagons, hexagons, and octagons.
This document defines and describes basic geometric shapes and terms. It defines points, lines, planes, angles, perpendicular and parallel lines, triangles, polygons, quadrilaterals like squares, rectangles, trapezoids and parallelograms, circles, cylinders, spheres, ovals, and properties like concurrent lines and types of quadrilaterals like rhombuses. Key geometric concepts and their definitions are provided to establish common understanding of shape names and characteristics.
This document defines common geometric terms including point, line, plane, angle, perpendicular lines, parallel lines, triangles, right triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, pyramids, cubes, and cones. It provides the basic definitions for these terms, stating that points have no size, lines have no thickness, planes extend forever, and polygons have a certain number of sides.
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cubes, and pyramids. It explains that a point has no size, a line has no thickness and extends forever, and a plane is a flat surface with no thickness that extends forever. Common shapes are also defined, such as triangles, rectangles, squares, and circles. Three-dimensional shapes like cylinders, spheres, cubes and pyramids are also described.
1) A point is something that has a position but no size, and defines endpoints of line segments or positions on a plane.
2) A line segment is a broken part of a line with two endpoints.
3) A plane is a flat surface created by at least three points, which are considered coplanar.
The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, cubes, pyramids and cones. It provides the formal definitions for these terms and shapes as undefined or basic terms in geometry without thickness or size limitations that extend indefinitely in some cases. The project involves taking photos of these shapes in the real world during a family trip to Austria.
This document defines and describes basic geometric shapes including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cubes and polygons. Key properties are outlined such as a point having no size, a line connecting two points, a plane extending forever, angles formed by rays, perpendicular and parallel lines, and characteristics of triangles, rectangles, trapezoids, parallelograms, circles, cylinders and spheres. Common polygons like pentagons, hexagons and octagons are also defined.
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, cubes, pyramids and cones. Key geometric concepts covered are undefined terms, polygons, perpendicular and parallel lines, circles, spheres, prisms and pyramids. Real world examples are not provided.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.