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Geometry Chapter 2: Reasoning and Proof 2.7 Prove Angle Pair Relationships SWBAT: Use properties of special pairs of angles. Common Core: G.CO.9; G.CO.10; G.CO.10; G.CO.11 Theorem 2.3: Right Angles Congruence Theorem All right angles are _____________________________________________. Example 1: Use right angle Congruence Given: π½πΎ β₯ πΎπΏ, ππΏ β₯ πΎπΏ Prove: β πΎ β β πΏ Statements Reasons 1. π½πΎ β₯ πΎπΏ, ππΏ β₯ πΎπΏ 1. 2. 2. Definition of perpendicular lines 3. β πΎ β β πΏ 3. Geometry Chapter 2: Reasoning and Proof Example 2: Use the congruence Supplements Theorem Given: β 1 πππ β 2 are supplements. β 1 πππ β 4 are supplements. πβ 2 = 45° Prove: πβ 4 = 45° Statements Reasons 1. β 1 πππ β 2 are supplements. β 1 πππ β 4 are supplements. 1. 2. 2. Congruent Supplements Theorem 3. πβ 2 = πβ 4 3. 4. πβ 2 = 45° 4. 5. 5. Substitution Property of Equality Geometry Chapter 2: Reasoning and Proof Example 3: Use the Vertical Angle Congruence Theorem Given: β 4 is a right angle Prove: β 2 πππ β 4 are supplementary Statements Reasons 1. β 4 is a right angle 1. 2. 2. Definition of a right angle 3. β 2 β β 4 3. 4. 4. Definition of congruent angles 5. πβ = 90° 5. 6. 6. πβ 2 + πβ 4 = 180° Geometry Chapter 2: Reasoning and Proof Example 4: Write and solve an equation to find x. Use x to find πβ πΉπΎπΊ. Homework: Practice 2.7B