Unit 1 day 8 a
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The document discusses linear angles and deductive reasoning in geometry. It includes warmups and worksheets on labeling angles, exploring properties of angles when parallel lines are cut by a transversal. These properties include corresponding angles being congruent, same-side exterior angles and alternate interior angles being supplementary. The document provides guidance on writing geometric proofs to show statements are true for all cases using justification, definitions, and relationships between angles. It concludes with preparing for a quiz by summarizing mathematics and checking understanding.
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Pairs of angles formed by parallel lines cut by a transversal
This document discusses parallel lines cut by a transversal and defines three types of angle pairs formed:
1) Alternate interior angles are non-adjacent interior angles on opposite sides of the transversal.
2) Alternate exterior angles are non-adjacent exterior angles on opposite sides of the transversal.
3) Corresponding angles are non-adjacent angles, with one interior and one exterior, on the same side of the transversal.
The document provides an example figure and instructions to draw parallel lines cut by a transversal, name the three types of angle pairs, and measure them.
Teacher Lecture
This document provides a lesson on parallel lines cut by a transversal. It defines key terms like transversal, parallel lines, interior angles, and exterior angles. It then explains the angle relationships that occur when parallel lines are cut by a transversal, including:
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The document defines and provides examples of parallel lines, transversals, and the different types of angles formed by parallel lines intersected by a transversal, including interior angles, exterior angles, corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles, and same-side exterior angles. It then gives an activity where students label locations on a map using different angle relationships and fill in blanks to identify angle names.
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The document provides definitions and examples of different types of angles formed when a transversal line crosses two or more parallel lines, including alternate exterior angles, alternate interior angles, corresponding angles, same-sided interior angles, same-sided exterior angles, and vertical angles. Students act as vocabulary detectives to find and leave clues about the definitions of each term posted around the room. As homework, students are asked to complete a handout defining and practicing identifying the different types of angles.
Planes, Lines and Transversals
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This document discusses parallel lines cut by a transversal and the angle relationships that are formed. It defines key terms like transversal, interior angles, exterior angles, corresponding angles, same-side interior angles, alternate interior angles, same-side exterior angles, and alternate exterior angles. The main points are that when parallel lines are cut by a transversal, alternate interior angles are congruent, alternate exterior angles are congruent, same-side interior angles are supplementary, and same-side exterior angles are supplementary. Examples are provided to illustrate these relationships.
Angles formed by parallel lines cut by transversal
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.
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This document discusses parallel lines cut by a transversal and defines three types of angle pairs formed:
1) Alternate interior angles are non-adjacent interior angles on opposite sides of the transversal.
2) Alternate exterior angles are non-adjacent exterior angles on opposite sides of the transversal.
3) Corresponding angles are non-adjacent angles, with one interior and one exterior, on the same side of the transversal.
The document provides an example figure and instructions to draw parallel lines cut by a transversal, name the three types of angle pairs, and measure them.
Teacher Lecture
This document provides a lesson on parallel lines cut by a transversal. It defines key terms like transversal, parallel lines, interior angles, and exterior angles. It then explains the angle relationships that occur when parallel lines are cut by a transversal, including:
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This document discusses parallel lines cut by a transversal and the angle relationships that are formed. It defines key terms like transversal, interior angles, exterior angles, corresponding angles, same-side interior angles, alternate interior angles, same-side exterior angles, and alternate exterior angles. The main points are that when parallel lines are cut by a transversal, alternate interior angles are congruent, alternate exterior angles are congruent, same-side interior angles are supplementary, and same-side exterior angles are supplementary. Examples are provided to illustrate these relationships.
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This document defines key terms related to parallel lines and transversals, including transversal, interior angles, exterior angles, alternate interior angles, consecutive interior angles, and corresponding angles. It states the theorems that if two parallel lines are cut by a transversal, then each pair of alternate interior angles, consecutive interior angles, alternate exterior angles, and corresponding angles are congruent.
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This document discusses parallel lines and transversals. It defines a transversal as a line that intersects two or more parallel lines at different points. It then explains the four properties of parallel lines cut by a transversal:
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2) Alternate interior angles are congruent
3) Interior angles on the same side of the transversal are supplementary
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Examples are given to illustrate each property. The document also discusses how transversals can connect parallel aspects of life, like people.
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- 1. LINEAR ANGLES August 16th Learning outcome: How do we use deductive reasoning to proficiently justify geometric properties?
- 2. WARMUP: LINEAR ANGLES WORKSHEET
- 4. EXPLORE - PAGE 36 #4 Given Linear Pair Postulate Corresponding Angles Substitution Definition of Supplementary If two parallel lines are cut by a transversal, then __________________ angles are _____________________. Vertical Angle Theorem
- 5. EXPLORE - PAGE 37 #5 If two parallel lines are cut by a transversal, then same-side exterior angles are ________________. If two parallel lines are cut by a transversal, then alternate interior angles are _________________. If two parallel lines are cut by a transversal, then alternate exterior angles are _________________. Given Linear Pair Postulate Corresponding Angles Assumption Substitution Definition of Supplementary Vertical Angle Theorem
- 6. SUMMARY - GALLERY WALK Were the requirements of a proficient proof met? Does the argument have any errors? Does it show the statement is true for all numbers or for some numbers? Does the argument show why the statement is true? Does the argument provide an easy way to convince a skeptic? Return to your proof and read your feedback. Write a final draft of your proof.
- 7. TOOLKIT Justifcation Statement Definition OR If-Then Statement Picture Relationship (Congruent OR Supplementar y) Check when ready to be used in a proof Corresponding Angles Postulate Alternate Interior Angles Postulate Alternate Exterior Angles Postulate Same-Side Interior Angles Postulate Same-Side Exterior
- 8. CLASSWORK – P. 32-33 #3 C
- 9. CLASSWORK – P. 32-33 #3 C
- 10. SUMMARY PREPARE FOR QUIZ p. 15 1. Summarize the mathematics 2. Check your understanding