Honors Geometry Chapter 3 – Proofs Involving Parallel and Perpendicular Lines Practice – Proofs Involving Parallel and Perpendicular Lines No Textbook Correlation Name ________________________ Date ________________ Period _______ Choose the word(s) that best completes the statements. 1. If two lines are cut by a transversal so that alternate interior angles are (congruent, supplementary, complementary), then the lines are parallel. 2. If two lines are cut by a transversal so that same-side interior angles are (congruent, supplementary, complementary), then the lines are parallel. 3. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles are congruent, then the lines are parallel. 4. If two coplanar lines are perpendicular to the same line, then the two lines are (perpendicular, parallel, skew) to each other. a || b. State the postulate or theorem that justifies each conclusion. a 1 2 Example: 48 because || lines corresponding s 3 4 5. 18 _________________________________ b 5 6 7 8 6. 37 _________________________________ 7. 4 supplementary to 6 _________________________________ 8. 3 supplementary to _________________________________ 9. 76 ________________________________ State the postulate or theorem (shorthand) that allows you to conclude that j || k. Example: corr. ‘s // lines 10. ________________ 11. ________________ 12. ________________ 13. ________________ ________________ ________________ ________________ ________________ j j 120 75 j 80 k k 110 80 70 k 120 k 75 j Use the figure and the given information to determine which lines, if any, are parallel. Justify using a theorem or postulate. a 14. 9 16 ___ || ___ because ________________________ 1 5 2 6 b 15. 57 ___ || ___ because _________________________ 9 3 13 10 7 4 14 8 11 16. 14 16 ___ || ___ because _______________________ 15 12 c 16 17. 1 16 ___ || ___ because _______________________ d 18. 5 10 ___ || ___ because ________________________ Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines Fill in the missing statements and reasons in each proof shown below. You must mark the diagram for credit. 19. Given: ab Statements Reasons cd 1) 1) given Prove: 1 16 2) 18 2) a 3) 3) given 1 5 2 6 b 4) 8 16 4) 9 3 13 10 7 4 5) 5) Transitive prop. 14 8 11 15 12 c 16 d 20. Given: Statements Reasons 1) 1) given (be careful) Prove: 98 2) 96 2) a 3) 3) given 1 5 2 6 b 4) 4) 9 3 13 1 0 7 4 5) 5) 14 8 11 15 12 c 16 d 21. Given: o a Prove: mm2 11 180 1 5 2 Statements Reasons 6 b 9 3 1) 1) given 13 10 7 4 14 8 11 2) 2 & 3 are supplementary 2) 15 12 c 16 3) 3) d 4) 4) 5) 5) 6) 6) 7) 7) Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines 22. Given: lm 17 l m Prove: ab 1 2 3 a 4 Statements Reasons 1) 1) given 5 7 6 b 2) 2) 3) 3) 4) 4) 5) 5) l m 23. Given: 1 2 3 a 5 is supplementary to 2 4 Prove: 5 7 6 b Statements Reasons 1) supplementary 1) 2) 2) 3) 3) 4) 15 4) 5) 5) 6) mm1 2 180o 6) 7) 7) 8) 8) 24. Given: 12 pq p q Prove: qa a 1 2 Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines 25. Given: 1 &2are Complementary Prove: SX WX X S 1 • 2 Statements Reasons 1) 1 & 2 are Complementary 1) 2) mm1 2 90 2) W • 3) m WXS m 12 m 3) 4) m WXS 90 4) 5) WXS is right 5) 6) SX WX 6) 26. Prove the statement: If two parallel lines are cut by a transversal, then the same-side exterior angles are supplementary. m n Given: _________________________ Prove: _________________________ 1 2 3 a Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6) 7) 7) 27. Prove the statement: If two coplanar lines are perpendicular, then they form a pair of congruent, supplementary angles. First write the given(hypothesis) and the prove(conclusion) using the diagram. Given: _________________________ Prove: _________________________ and ____________________________ Statements Reasons m 1) 1) 2) 2) 1 2 n 3) 3) 4) 4) 5) 5) 6) 6) .