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Lesson 2.6: Parallel Lines Proofs Worksheet Honors Geometry Mr. Ferwerda Name: 1. Without using a protractor, find the measures of all the lettered angles. [Given: l3 l2 a e d g l m j i c b f y z α k l4 126° l1 h l1 // l 2; l 3 // l 4] n β x w γ δ s q o p r l5 157° u t 149° In problems 2 – 6, write complete proofs. 2. Prove the Alternate Exterior Angles Theorem: l 1 3 If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent. m Given: l // Prove: ∠2 ≅ ∠7 7 8 m Conclusions 5 Justifications 6 2 4 Lesson 2.6: Parallel Lines Proofs Worksheet 3. page 2 Prove the Same Side Exterior Angles Theorem: l 1 If 2 parallel lines are cut by a transversal, then the same side exterior angles are supplementary. 3 5 6 7 8 m Given: l // Prove: ∠1 and ∠7 are supplementary m Conclusions Justifications m l 4. Given: Prove: ∠1 ≅ ∠2 ∠1 ≅ ∠4 l // m Conclusions 3 2 1 Justifications 4 2 4 Lesson 2.6: Parallel Lines Proofs Worksheet 5. Given: l // Prove: ∠4 ≅ ∠10 m; // m n page 3 1 4 2 3 l Conclusions 6. 9 12 5 8 6 7 m 10 11 n Justifications Prove the Transitivity of Parallels Theorem: If 2 lines are parallel to the same line, then those lines are parallel to each other. 1 a 2 b [Hint: use the numbered angles!] Given: a // b; Prove: a // c b // Conclusions c c Justifications 3