1 / 7

2.5 Angle Relationships

2.5 Angle Relationships. Objectives: I CAN apply the Linear Pair Conjecture and Vertical Angle Conjecture to solve geometric problems. I CAN write logical explanations in the form of paragraph proofs. Serra - Discovering Geometry Chapter 2: Reasoning in Geometry. Conjecture 1.

danil
Download Presentation

2.5 Angle Relationships

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 2.5 Angle Relationships Objectives: I CAN apply the Linear Pair Conjecture and Vertical Angle Conjecture to solve geometric problems. I CAN write logical explanations in the form of paragraph proofs. Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  2. Conjecture 1 Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  3. Conjecture 2 Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  4. C-1: Linear Pair Conjecture Linear pairs are supplementary. If two angles form a linear pair, then they are supplementary. If Then Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  5. C-2: Vertical Angles Conjecture Vertical angles are congruent. If two angles are vertical angles, then they are congruent. If Then Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  6. Proof of Conjecture 2: Vertical Angles Conjecture Reasons Statements 1. Given 2. Linear Pair Conjecture (C-1) 3. Substitution 4. Subtraction Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

  7. Proof of Conjecture 2: Vertical Angles Conjecture Angles 1 and 2 and angles 2 and 3 form linear pairs. According to the Linear Pair Conjecture, and . By substituting, we get . According to the subtraction property of equality, you can subtract angle 2 from both sides, so . Thus the vertical angles are congruent. Serra - Discovering Geometry Chapter 2: Reasoning in Geometry

More Related