TechMathI - 1.5
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This document provides definitions and examples of common geometric figures including rays, line segments, points, planes, lines, angles, parallel lines, and perpendicular lines. It asks students to name pairs of lines that appear parallel or perpendicular using both symbols and words.
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3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
Geometry scrapbook Meta Thurman
The document is Meta Thurman's scrapbook from November 19th 2012. It discusses various geometry concepts like parallel lines, congruent objects, vertical angles, perpendicular lines, intersecting lines, supplementary angles, different proportions, adjacent angles, similarity, 2D and 3D shapes, surface area, Pythagorean theorem, diameter, and volume. Many of the concepts are related to diagrams of horses, fences, and tack for horseback riding to explain their practical applications.
Adjacent and Vertical Angles
Two angles are adjacent if they share a common side and vertex. Vertical angles are angles opposite each other formed when two lines intersect, and they are congruent. This document discusses adjacent angles, vertical angles, and uses examples like naming angles and determining missing angle measures to teach properties of these angle types.
2.2 definitions and biconditionals
The document discusses definitions, biconditional statements, and their use in geometry. It provides examples of:
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2) Analyzing statements about a diagram for truth based on definitions.
3) Rewriting conditional statements as biconditional statements using "if and only if".
4) Identifying whether biconditional statements are true based on the truth of both the conditional statement and its converse.
1.2.2 Pairs of Angles
Identify linear pairs, vertical angles, complementary angles, and supplementary angles, and use their relationships to set up and solve equations.
Finding opposites and absolute value 2.1 (1)
- The opposites of numbers are points that are equidistant from zero on the number line but on opposite sides. For example, -3 and 3 are opposites.
- The absolute value of a number represents the distance between that number and zero on the number line, regardless of whether the number is positive or negative. The symbol for absolute value is | |.
- To find the absolute value of a negative number, take the number without the negative sign. For example, |-8| = 8.
- Opposites are numbers with the same magnitude but opposite signs. Absolute value gives the distance from zero without regard to sign.
Geometry Section 2-9
This document discusses proving that lines are parallel. It defines six postulates and theorems related to parallel lines, including the converse of corresponding angles, alternate exterior angles, consecutive interior angles, and alternate interior angles. An example problem demonstrates using the corresponding angles converse to show that two lines are parallel based on congruent corresponding angles. A second example finds the measure of an angle given that two lines are parallel based on the alternate interior angles theorem.
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This document defines and describes various geometric shapes including points, lines, angles, polygons, polyhedra, circles and spheres. It provides definitions for common geometric terms like line segments, rays, parallel and intersecting lines, acute, obtuse and right angles. It also defines types of triangles, quadrilaterals, regular and irregular polygons as well as three-dimensional shapes such as prisms, pyramids, cones, cylinders, cubes and spheres.
Recommended
3.1 notes
The document defines and describes various types of lines and angles. It defines parallel lines as lines that do not intersect and are coplanar. Skew lines do not intersect and are not coplanar. A transversal is a line that intersects two or more lines at different points, and can be used to define corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. The document also presents the parallel postulate and perpendicular postulate.
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The document is Meta Thurman's scrapbook from November 19th 2012. It discusses various geometry concepts like parallel lines, congruent objects, vertical angles, perpendicular lines, intersecting lines, supplementary angles, different proportions, adjacent angles, similarity, 2D and 3D shapes, surface area, Pythagorean theorem, diameter, and volume. Many of the concepts are related to diagrams of horses, fences, and tack for horseback riding to explain their practical applications.
Adjacent and Vertical Angles
Two angles are adjacent if they share a common side and vertex. Vertical angles are angles opposite each other formed when two lines intersect, and they are congruent. This document discusses adjacent angles, vertical angles, and uses examples like naming angles and determining missing angle measures to teach properties of these angle types.
2.2 definitions and biconditionals
The document discusses definitions, biconditional statements, and their use in geometry. It provides examples of:
1) Defining perpendicular lines and lines perpendicular to a plane.
2) Analyzing statements about a diagram for truth based on definitions.
3) Rewriting conditional statements as biconditional statements using "if and only if".
4) Identifying whether biconditional statements are true based on the truth of both the conditional statement and its converse.
1.2.2 Pairs of Angles
Identify linear pairs, vertical angles, complementary angles, and supplementary angles, and use their relationships to set up and solve equations.
Finding opposites and absolute value 2.1 (1)
- The opposites of numbers are points that are equidistant from zero on the number line but on opposite sides. For example, -3 and 3 are opposites.
- The absolute value of a number represents the distance between that number and zero on the number line, regardless of whether the number is positive or negative. The symbol for absolute value is | |.
- To find the absolute value of a negative number, take the number without the negative sign. For example, |-8| = 8.
- Opposites are numbers with the same magnitude but opposite signs. Absolute value gives the distance from zero without regard to sign.
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This document discusses proving that lines are parallel. It defines six postulates and theorems related to parallel lines, including the converse of corresponding angles, alternate exterior angles, consecutive interior angles, and alternate interior angles. An example problem demonstrates using the corresponding angles converse to show that two lines are parallel based on congruent corresponding angles. A second example finds the measure of an angle given that two lines are parallel based on the alternate interior angles theorem.
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TechMathI - 1.5
- 2. Parallel Lines Two lines are parallel if they are in the same plane and never intersect Symbol for Parallel Lines:
- 3. Perpendicular Lines Perpendicular lines are lines that intersect to form right angles. Symbol for Perpendicular Lines:
- 4. Name all pairs of lines that appear to be parallel and perpendicular. Use both symbols and words.
- 5. Name all pairs of lines that appear to be parallel and perpendicular. Use both symbols and words.