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HW-3.3 Practice B (1-8) www.westex.org HS, Teacher Websites 10-17-14 Warm up—Geometry H Finish the conditional statement below so that it is true and then write the converse of it. If two lines that are cut by a transversal are parallel then corresponding angles are _________. 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) www.westex.org HS, Teacher Websites Name _________________________ Date ________ Geometry Honors 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 HYPOTHESIS and CONCLUSION. The converse of a theorem is not automatically true. If it is true, it must be stated as a POSTULATE or PROVEN 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 Angle 4 and angle 8 are corr. angles ℓ || m CONVERSE of corr. angles postulate 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 substitution 40o = 3(30) – 50 = m7 substitution m3 = m7 transitive prop of equality 3 7 Definition of angles ℓ || m Converse of corr. angles postulate 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 _________________________ The PARALLEL POSTULATE guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ. 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 4 and 8 are alt. ext. s r || s Converse of alt. ext. s thm. 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 substitution m3 = 25x – 3 = 25(5) – 3 = 122o substitution m2 + m3 = 58° + 122° = 180o 2 & 3 are same side int. s r || s Conv. of same side int. s thm. 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° _______________ m7 = x + 50 = (50) + 50 = 100° _______________ 3 7 _______________ r || s _______________ Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m SEE the TYPO in PIC? You Try: Given: 1 4, 3 and 4 are supplementary. Prove: ℓ || m