Lesson 2.5. oning-diagonals-angles-and-parallel- lines/vertical-angles-problem-3/ Quick review:

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Presentation transcript:

Lesson 2.5

oning-diagonals-angles-and-parallel- lines/vertical-angles-problem-3/ Quick review:

Properties of Angle Congruence Angle congruence is reflexive, symmetric, and transitive. Examples: –Reflexive: For any angle A,  A ≅  A. –Symmetric: If  A ≅  B, then  B ≅  A –Transitive: If  A ≅  B and  B ≅  C, then  A ≅  C. Quick review:

Ex. 1: Transitive Property of Angle Congruence Prove the Transitive Property of Congruence for angles Given:  A ≅  B,  B ≅  C Prove:  A ≅  C A B C

Ex. 1: Transitive Property of Angle Congruence Statement: 1.  A ≅  B,  B ≅  C 2.m  A = m  B 3.m  B = m  C 4.m  A = m  C 5.  A ≅  C Reason: 1.Given 2.Def. Cong. Angles 3.Def. Cong. Angles 4.Transitive property 5.Def. Cong. Angles

Theorem 2.4 All right angles are congruent. Example 3: Proving Theorem 2.4 Given:  1 and  2 are right angles Prove:  1 ≅  2

Ex. 2: Statement: 1.  1 and  2 are right angles 2.m  1 = 90 , m  2 = 90  3.m  1 = m  2 4.  1 ≅  2 Reason: 1.Given 2.Def. Right angle 3.Transitive property 4.Def. Cong. Angles

Given: Statement: Reason: Prove: x =

Given: Statement: Reason: Prove: y =

Given: Statement: Reason: Prove: prove z =

Given: Statement: Reason: Prove: prove x =

Given: Statement: Reason: Prove: prove x =

Given: Statement: Reason: Prove: y =

HINT: Draw a picture 1 st !!!!