Honors Geometry Chapter 3 Proofs Involving Parallel and ...

1 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 .

2 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. Example: 48 because || lines corresponding s 5. 18 _____ 6. 37 _____ 7. 4 supplementary to 6 _____ 8. 3 supplementary to 4 _____ 9.

3 76 _____ State the postulate or theorem (shorthand) that allows you to conclude that j || k. Example: corr. s // lines 10. _____ 11. _____ 12. _____ 13. _____ _____ _____ _____ _____ Use the figure and the given information to determine which lines, if any, are Parallel . Justify using a theorem or postulate. 14. 916 ___ || ___ because _____ 15. 57 ___ || ___ because _____ 16. 1416 ___ || ___ because _____ 17.

4 116 ___ || ___ because _____ 18. 510 ___ || ___ because _____ 1 2 6 8 5 a b 3 4 7 j k 75 75 j k 110 70 j k 120 120 80 80 j k a d b c 1 5 2 3 7 6 16 8 4 13 12 11 10 9 15 14 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: 116 2) 18 2) 3) 3) given 4) 816 4) 5) 5) Transitive prop.

5 20. Given: ab Statements Reasons cd 1) 1) given (be careful) Prove: 98 2) 96 2) 3) 3) given 4) 4) 5) 98 5) 21. Given: ab cd Prove: 211 180omm Statements Reasons 1) 1) given 2) 2 & 3 are supplementary 2) 3) 3) 4) 4) 5) 5) 6) 6) 7) 7) a d b c 1 5 2 3 7 6 16 8 4 13 12 11 10 9 15 14 a d b c 1 5 2 3 7 6 16 8 4 13 12 11 10 9 15 14 a d b c 1 5 2 3 7 6 16 8 4 13 12 11 10 9 15 14 Honors Geometry .

6 Chapter 3 Proofs Involving Parallel and perpendicular Lines 22. Given: lm 17 Prove: ab Statements Reasons 1) lm 1) given 2) 2) 3) 3) 4) 4) 5) 5) 23. Given: ab 5 is supplementary to 2 Prove: lm Statements Reasons 1) 5 supplementary2 1) 2) 2) 3) ab 3) 4) 15 4) 5) 5) 6) 12 180omm 6) 7) 7) 8) lm 8) 24.

7 Given: 12 pq Prove: qa Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 2 m b a l 1 3 4 7 5 6 2 m b a l 1 3 4 7 5 6 2 q a p 1 Honors Geometry : Chapter 3 Proofs Involving Parallel and perpendicular Lines 25. Given:2&1 are Complementary Prove: WXSX Statements Reasons 1) 1 & 2 are Complementary 1) 2) 12 90mm 2) 3) 12m WXS mm 3) 4) 90m WXS 4) 5) WXS is right 5) 6) SXWX 6) 26.

8 Prove the statement: If two Parallel lines are cut by a transversal, then the same-side exterior angles are supplementary. Given: _____ Prove: _____ 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 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6) W X S 1 2 2 n a m 1 3 2 m n 1