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HW-3.3 Practice B (1-8) 3.1-3.3 Quiz THU 10-23 www.westex.org HS, Teacher Websites 10-20-14 Warm up—Geometry CPA Line h and line j are parallel. Find all the missing angles. 49o 2 3 4 h 5 6 7 8 j GOAL: I will be able to: 1. use the angles formed by a transversal to prove two lines are parallel. HW-3.3 Practice B (1-8) 3.1-3.3 Quiz THU 10-23 www.westex.org HS, Teacher Websites Name _________________________ Date ________ Geometry CPA 3.3 Proving Lines Parallel GOAL: I will be able to: 1. use the angles formed by a transversal to prove two lines are parallel. The converse of a theorem is found by exchanging the _______________ and _______________. The converse of a theorem is not automatically true. If it is true, it must be stated as a ______________ or ______________ as a separate theorem. Example 1: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 4 8 4 8 _________________________ ℓ || m _________________________ You Try: Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 1 3 1 3 __________________________ ℓ || m __________________________ Example 1B: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40o _________________________ 40o = 3(30) – 50 = m7 _________________________ _______________ _________________________ _______________ _________________________ ℓ || m _________________________ You Try: Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m7 = (4x + 25)°, m5 = (5x + 12)°, x = 13 m7 = 4(13) + 25 = 77o _________________________ 77o = 5(13) + 12 = m5 _________________________ _______________ _________________________ _______________ _________________________ ℓ || m _________________________ Example 2: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. 4 8 4 8 _______________ r || s _______________ You Try Use the given information and the theorems you have learned to show that r || s. 2 6 2 6 _______________ r || s _______________ Example 2B: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 m2 = 10x + 8 = 10(5) + 8 = 58o _______________ m3 = 25x – 3 = 25(5) – 3 = 122o _______________ m2 + m3 = 58° + 122° = 180o _______________ r || s _______________ You Try: Use the given information and the theorems you have learned to show that r || s. m3 = 2x, m7 = (x + 50), x = 50 m3 = 2x = 2(50) = 100° _______________ 100°= x + 50 = (50) + 50 = m7 _______________ m3 = m7 _______________ 3 7 _______________ r || s _______________ Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m FIND THE TYPO IN THE PICTURE!!!