Parallel Lines

Parallel Lines

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1. In the accompanying diagram, lines a and b are 4. Which geometric principle is used to justify the parallel, and lines c and d are transversals. Which construction below? angle is congruent to angle 8?

A. A line perpendicular to one of two parallel lines is perpendicular to the other.

B. Two lines are perpendicular if they intersect A. 6 B. 5 C. 3 D. 4 to form congruent adjacent angles.

C. When two lines are intersected by a 2. Lines j and k intersect at point P. Line m is transversal and alternate interior angles are drawn so that it is perpendicular to lines j and k congruent, the lines are parallel. at point P. Which statement is correct? D. When two lines are intersected by a transversal and the corresponding angles are A. Lines j and k are in perpendicular planes. congruent, the lines are parallel. m j k B. Line is in the same plane as lines and . ←→ ←→ ←→ ←→ 5. In the accompanying diagram, AB k CD, EF k GH, C. Line m is parallel to the plane containing and m∠1 = 105. What is m∠2? lines j and k.

D. Line m is perpendicular to the plane containing lines j and k.

←→ AB 3. In←→ the accompanying←→ diagram, ←→is parallel←→ to CD and transversal EF intersects AB and CD at G and H, respectively. If m∠DHG : m∠BGH = 1 : 2, find m∠DHG.

←→ RS 6. In the accompanying diagram,←→ transversal←→ intersects parallel lines XY and WZ at E and H, respectively. If m∠HEY = 72, what is m∠ZHS ?

page 1 ←→ ←→ ←→ 7. Transversal EF intersects AB and CD, as shown in 10. The accompanying diagram shows two parallel the diagram below. streets, Main Street and Brooks Road, intersected by Jay Street. The obtuse angle that Jay Street forms with Brooks Road is three times the measure of the acute angle that Jay Street forms with Main Street.

←→Which←→ statement could always be used to prove AB k CD? What is the measure of the acute angle formed by ∼ Jay Street and Main Street? A. ∠2 = ∠4

∠ ∼ ∠ ◦ ◦ ◦ ◦ B. 7 = 8 A. 45 B. 60 C. 90 D. 135 C. ∠3 and ∠6 are supplementary ←→ ←→ AB CD D. ∠1 and ∠5 are supplementary 11. In the accompanying←→ diagram,←→ and ←→ are parallel and EF intersects AB at G and CD at H. If m∠AGH = 80, what is m∠CHG ? 8. In the accompanying diagram, line ` is parallel to line m, and line t is a transversal.

Which must be a true statement? 12. In the diagram below, lines n and m are cut by transversals p and q.

A. m∠1 + m∠4 = 180 B. m∠1 + m∠8 = 180

C. m∠3 + m∠6 = 180 D. m∠2 + m∠5 = 180

←→ ←→ AB k CD 9. In←→ the accompanying←→ ←→ diagram, , EF intersects AB and CD, and the ratio of m∠r to m∠s is 1 : 4. Find m∠r.

Which value of x would make lines n and m parallel?

A. 110 B. 80 C. 70 D. 50

page 2 Parallel Lines ←→ AB 17. In the accompanying diagram, line k is parallel to 13. In←→ the accompanying←→ ←→ diagram, is parallel CD AB CD line n, and line ` is a transversal that intersects ←→to , and and are cut by transversal EF at points G and H, respectively. If lines k and n. If m∠1 = x + 25 and m∠2 = 5x − 25, m∠EGA = (2x + 30) and m∠EHC = (x + 80), find x. find x.

←→ ←→ −−− AB k CD EF 18. In the accompanying←→ diagram,←→ −−−−, intersects AB at E and CD at F, and GH intersects 14. In the accompanying diagram, transversal t ←→ −−− AB at G and EF at H. If m∠EGH = 40, intersects parallel lines ` and m. If m∠1 = 2x + 40 m∠GHE = 80, and m∠EFD = x, what is the value and m∠2 = 3x + 20, find the value of x. of x ?

←→ ` k m t s 15. In the accompanying diagram, transversal EF 19. In the accompanying diagram, , and ←→ ←→ m∠ intersects parallel lines AB and CD at G and are intersecting transversals, 1 = 130, and m∠ m∠ H, respectively. If m∠EGB = 2x + 40 and 2 = 60. Find 3. m∠FHC = 3x − 10, what is the value of x?

←→ ←→ −−→ −−− 20. In the accompanying diagram, AB k CD, 16. In the accompanying diagram, DH k EF. If m∠CAB = 80, and m∠DCB = 40. m∠HDF = 30 and m∠EDF = 55, find m∠E.

What is m∠ACB?

A. 40 B. 60 C. 80 D. 120

page 3 Parallel Lines ←−−→ ←→ 21. Line n intersects lines l and m, forming the angles EGF AB 24. In←→ the accompanying−−− figure,←→ ←→intersects and shown in the diagram below. CD, and AG is drawn. If AB k CD, m∠FED = x, m∠GAF = 2x, and m∠FGA = 3x, find x.

←→ ←→ 25. In the accompanying diagram, AC k CD, m∠x = 50, y z Which value of x would prove l k m? and m∠ = 60. What is m∠ ?

A. 2.5 B. 4.5 C. 6.25 D. 8.75

22. Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the accompanying diagram. Find the number of degrees in the acute angle formed by the intersection of Walnut Street and Elm Street. −−− AB 26. In the accompanying diagram,←→ ←→ is extended to C, m∠DBC = 142, and AE k DB. Find m∠EAB.

←→ AB 23. In←→ the accompanying diagram, is a parallel to CD, m∠BAC = 46, and m∠BCD = 65. Find the measure of ∠ACB.

−−− −−− 27. In the diagram below, ` k m and QR ⊥ ST at R.

If m∠1 = 63, find m∠2.

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Parallel Lines 08/15/2015 1. 21. Answer: A Answer: B 2. 22. Answer: D Answer: 65 3. 23. Answer: 60 Answer: 69 4. 24. Answer: D Answer: 30 5. 25. Answer: 105 Answer: 110 6. 26. Answer: 72 Answer: 38 7. 27. Answer: C Answer: 27 8. Answer: D 9. Answer: 36 10. Answer: A 11. Answer: 100 12. Answer: C 13. Answer: 50 14. Answer: 20 15. Answer: 50 16. Answer: 95 17. Answer: 30 18. Answer: 60 19. Answer: 70 20. Answer: B