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Lesson 2.4 - Reasoning in Algebra Lesson 2.5 - Proving Angles Congruent “The other day I was driving down the road and saw a banana peel…and swerved. Thank you Mario Kart.” Properties (on theorem sheet) Properties (on theorem sheet) Justifying Steps Example: Solve for x. JUSTIFY each step. Statement 2(x - 3) +12 = 14 2x – 6 + 12 = 14 2x + 6 = 14 2x = 8 x=4 Reason Given Justifying Steps Example: Solve for x and justify each step. B Given: mAOC 139 A x (2x+10) C O Statement mAOC 139 mAOB mBOC mAOC x + 2x + 10 = 139 3x + 10 = 139 3x = 129 x = 43 Reason Justifying Steps Example: Solve for m and justify each step 2m Given: XZ = 32 X Statement XZ = 32 XY + YZ = XZ 2m + 5m + 11 = 32 7m + 11 = 32 7m = 21 m=3 5m + 11 Y Z Reason Vertical Angles Theorem Theorem: A statement that is proven Theorem 2.1: Vertical angles are congruent Prove it! Given:1 and 2 Prove: 1 2 are vertical angles Statement 1 and 2 are vertical angles m1 m3 180 m2 m3 180 m1 m3 m2 m3 m1 m2 1 2 1 3 4 2 Reason Finding Angle Measures Find the value of x. Then label all the angle measures. (7x – 6)o (2x + 9)o Finding Angle Measures Find the value of the variables. Then label all the angle measures (5x + 10)o (7x - 16)o (7x + 2y)o (8x + 9)o (19x)o Congruent Supplements Theorem Theorem 2.2: If two angles are supplements to the same angle, then the two angles are congruent 1 is supplementary to 2 3 is supplementary to 2 What can we conclude? 2 3 1 4 Congruent Complements Theorem Theorem 2.3: If two angles are complements of the same angle then they are congruent Theorem 2.4: All right angles are congruent Theorem 2.5: If two angles are congruent and supplementary, then each is a right angle Lesson 2.4 - Reasoning in Algebra Lesson 2.5 - Proving Angles Congruent HW: 2.4 # 2-22 even, 28, 44-49 2.5 # 1-3, 7-18, 21, Challenge: 30, 32 Tools: Vertical Angles Theorem, Congruent Supplements Theorem, Congruent Complements Theorem “The other day I was driving down the road and saw a banana peel…and swerved. Thank you Mario Kart.”