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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.

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2.5 Angle Relationships

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  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

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