Download 2.7 Prove Angle Pair Relationships

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: 𝐽𝐾 ⊥ 𝐾𝐿, 𝑀𝐿 ⊥ 𝐾𝐿 Prove: ∠𝐾 ≅ ∠𝐿 Statements Reasons 1. 𝐽𝐾 ⊥ 𝐾𝐿, 𝑀𝐿 ⊥ 𝐾𝐿 1. 2. 2. Definition of perpendicular lines 3. ∠𝐾 ≅ ∠𝐿 3. Geometry Chapter 2: Reasoning and Proof Example 2: Use the congruence Supplements Theorem Given: ∠1 𝑎𝑛𝑑 ∠2 are supplements. ∠1 𝑎𝑛𝑑 ∠4 are supplements. 𝑚∠2 = 45° Prove: 𝑚∠4 = 45° Statements Reasons 1. ∠1 𝑎𝑛𝑑 ∠2 are supplements. ∠1 𝑎𝑛𝑑 ∠4 are supplements. 1. 2. 2. Congruent Supplements Theorem 3. 𝑚∠2 = 𝑚∠4 3. 4. 𝑚∠2 = 45° 4. 5. 5. Substitution Property of Equality Geometry Chapter 2: Reasoning and Proof Example 3: Use the Vertical Angle Congruence Theorem Given: ∠4 is a right angle Prove: ∠2 𝑎𝑛𝑑 ∠4 are supplementary Statements Reasons 1. ∠4 is a right angle 1. 2. 2. Definition of a right angle 3. ∠2 ≅ ∠4 3. 4. 4. Definition of congruent angles 5. 𝑚∠ = 90° 5. 6. 6. 𝑚∠2 + 𝑚∠4 = 180° Geometry Chapter 2: Reasoning and Proof Example 4: Write and solve an equation to find x. Use x to find 𝑚∠𝐹𝐾𝐺. Homework: Practice 2.7B