Parallel Lines Practice

Parallel Lines Name: 1. In the accompanying diagram, lines a and b are parallel, and lines c and d are transversals. Which angle is congruent to angle 8? A. 2. Date: 6 B. 5 C. 3 4. D. 4 Lines j and k intersect at point P. Line m is drawn so that it is perpendicular to lines j and k at point P. Which statement is correct? A. Lines j and k are in perpendicular planes. B. Line m is in the same plane as lines j and k. C. Line m is parallel to the plane containing lines j and k. Which geometric principle is used to justify the construction below? A. A line perpendicular to one of two parallel lines is perpendicular to the other. B. Two lines are perpendicular if they intersect to form congruent adjacent angles. C. When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel. D. When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel. 5. ! ! ! ! In the accompanying diagram, AB k CD, EF k GH, and mO1 = 105. What is mO2? 6. ! In the accompanying diagram, transversal RS ! ! intersects parallel lines XY and WZ at E and H, respectively. If mOHEY = 72, what is mOZHS ? D. Line m is perpendicular to the plane containing lines j and k. 3. ! In the accompanying diagram, AB is parallel to ! ! ! ! CD and transversal EF intersects AB and CD at G and H, respectively. If mODHG : mOBGH = 1 : 2, nd mODHG. page 1 7. ! ! ! Transversal EF intersects AB and CD, as shown in the diagram below. 10. The accompanying diagram shows two parallel 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. O2 = O4 B. O7 = O8 C. O3 and O6 are supplementary A. D. O1 and O5 are supplementary 8. 9. A. mO1 + mO4 = 180 B. C. mO3 + mO6 = 180 D. mO2 + mO5 = 180 B. 60 C. 90 D. 135 11. ! In the accompanying diagram, AB and ! ! parallel and EF intersects AB at G and If mOAGH = 80, what is mOCHG ? 12. In the diagram below, lines n and m are cut by transversals p and q. In the accompanying diagram, line ` is parallel to line m, and line t is a transversal. Which must be a true statement? 45 ! CD are ! CD at H. mO1 + mO8 = 180 ! ! In the accompanying diagram, AB k CD, ! ! ! EF intersects AB and CD, and the ratio of mOr to mOs is 1 : 4. Find mOr. Which value of x would make lines n and m parallel? A. page 2 110 B. 80 C. 70 D. 50 Parallel Lines 13. ! In the accompanying diagram, AB is parallel ! ! ! to CD, and AB and CD are cut by transversal ! EF at points G and H, respectively. If mOEGA = (2x + 30) and mOEHC = (x + 80), nd x. 14. In the accompanying diagram, transversal t intersects parallel lines ` and m. If mO1 = 2x + 40 and mO2 = 3x + 20, nd the value of x. 15. ! In the accompanying diagram, transversal EF ! ! intersects parallel lines AB and CD at G and H, respectively. If mOEGB = 2x + 40 and mOFHC = 3x 10, what is the value of x? 16. ! In the accompanying diagram, DH k EF. If mOHDF = 30 and mOEDF = 55, nd mOE. 17. In the accompanying diagram, line k is parallel to line n, and line ` is a transversal that intersects lines k and n. If mO1 = x + 25 and mO2 = 5x 25, nd x. 18. ! ! In the accompanying diagram, AB k CD, EF ! ! intersects AB at E and CD at F, and GH intersects ! AB at G and EF at H. If mOEGH = 40, mOGHE = 80, and mOEFD = x, what is the value of x ? 19. In the accompanying diagram, ` k m, t and s are intersecting transversals, mO1 = 130, and mO2 = 60. Find mO3. 20. ! ! In the accompanying diagram, AB k CD, mOCAB = 80, and mODCB = 40. What is mOACB? A. page 3 40 B. 60 C. 80 D. 120 Parallel Lines 21. Line n intersects lines l and m, forming the angles shown in the diagram below. Which value of x would prove l k m? A. 22. 23. 2.5 B. 4.5 C. 6.25 24. ! ! In the accompanying gure, EGF intersects AB and ! ! ! CD, and AG is drawn. If AB k CD, mOFED = x, mOGAF = 2x, and mOFGA = 3x, nd x. 25. ! ! In the accompanying diagram, AC k CD, mO x = 50, and mOy = 60. What is mOz ? 26. In the accompanying diagram, AB is extended ! ! to C, mODBC = 142, and AE k DB. Find mOEAB. 27. In the diagram below, ` k m and QR ? ST at R. D. 8.75 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. ! In the accompanying diagram, AB is a parallel to ! CD, mOBAC = 46, and mOBCD = 65. Find the measure of OACB. If mO1 = 63, nd mO 2. page 4 Parallel Lines Problem-Attic format version 4.4.220 c 2011–2014 EducAide Software _ Licensed for use by Gregory Fisher Terms of Use at www.problem-attic.com Parallel Lines 08/15/2015 1. Answer: A 21. Answer: B 2. Answer: D 22. Answer: 65 3. Answer: 60 23. Answer: 69 4. Answer: D 24. Answer: 30 5. Answer: 105 25. Answer: 110 6. Answer: 72 26. Answer: 38 7. Answer: C 27. 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