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Name: ________________________ Class: ___________________ Date: __________ Geometry - Chapter 3 Corrective #1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine whether the lines 12x − 4y = −3 and y = x + 5 are parallel, intersect, or coincide. a. parallel c. coincide b. intersect ____ 2. Identify a pair of skew segments. a. b. AB & EF FB & AB c. d. 1 AB & HG DH & FG ID: A ____ 3. In a swimming pool, two lanes are represented by lines l and m. If a string of flags strung across the lanes is represented by transversal t, and x = 10, show that the lanes are parallel. a. b. c. d. 3x + 4 = 3(10) + 4 = 34°; 4x − 6 = 4(10) − 6 = 34° The angles are alternate interior angles and they are congruent, so the lanes are parallel by the Alternate Interior Angles Theorem. 3x + 4 = 3(10) + 4 = 34°; 4x − 6 = 4(10) − 6 = 34° The angles are alternate interior angles, and they are congruent, so the lanes are parallel by the Converse of the Alternate Interior Angles Theorem. 3x + 4 = 3(10) + 4 = 34°; 4x − 6 = 4(10) − 6 = 34° The angles are corresponding angles and they are congruent, so the lanes are parallel by the Converse of the Corresponding Angles Postulate. 3x + 4 = 3(10) + 4 = 34°; 4x − 6 = 4(10) − 6 = 34° The angles are same-side interior angles and they are supplementary, so the lanes are parallel by the Converse of the Same-Side Interior Angles Theorem. Short Answer 4. Give an example of same side interior angles. 2 5. Use the slope formula to determine the slope of the line. Show your work. NO work, NO credit. 6. Use the information m∠1 = (4x + 50)°, m∠2 = (8x − 10)°, and x = 15 , and the theorems you have learned to show that j Ä k . j 1 k 2 m 3 7. Graph the line y − 6 = 5(x − 3) . 8. Find m∠SUV . 4 9. Identify the transversal and classify the angle pair ∠1 and ∠6. Matching Match each vocabulary term with its definition. a. vertical angles b. alternate interior angles c. corresponding angles d. supplementary angles e. transversal f. same-side interior angles g. alternate exterior angles ____ 10. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and between the other two lines ____ 11. for two lines intersected by a transversal, a pair of angles that are on the same side of the transversal and between the two lines ____ 12. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and outside the other two lines ____ 13. a line that intersects two coplanar lines at two different points ____ 14. for two lines intersected by a transversal, a pair of angles that are on the same side of the transversal and on the same sides of the other two lines 5 Match each vocabulary term with its definition. a. x-intercept b. point-slope form c. rise d. run e. y-intercept f. distance from a point to a line g. slope-intercept form h. slope ____ 15. y − y 1 = m(x − x 1 ) , where m is the slope and (x 1 , y 1 ) is a point on the line ____ 16. the length of the perpendicular segment from the point to the line ____ 17. the difference in the y-values of two points on a line ____ 18. the difference in the x-values of two points on a line ____ 19. a line with slope m and y-intercept b can be written in the form y = mx + b ____ 20. a measure of the steepness of a line Match each vocabulary term with its definition. a. parallel lines b. parallel planes c. perpendicular lines d. skew lines e. perpendicular bisector f. perpendicular planes g. angle bisector ____ 21. lines that intersect at 90° angles ____ 22. a line perpendicular to a segment at the segment’s midpoint ____ 23. lines in the same plane that do not intersect ____ 24. planes that do not intersect ____ 25. lines that are not coplanar 6 ID: A Geometry - Chapter 3 Corrective #1 Answer Section MULTIPLE CHOICE 1. ANS: B 2. ANS: D 3. ANS: B TOP: 3-6 Lines in the Coordinate Plane TOP: 3-1 Lines and Angles TOP: 3-3 Proving Lines Parallel SHORT ANSWER 4. ANS: ∠8 and ∠4 TOP: 3-1 Lines and Angles 5. ANS: 7 −2 TOP: 3-5 Slopes of Lines 6. ANS: By substitution, m∠1 = 3(20) + 30 = 90° and m∠2 = 5(20) − 10 = 90° . By the Substitution Property of Equality, m∠1 = m∠2 = 90° . By the Converse of the Alternate Interior Angles Theorem, l Ä m. TOP: 3-3 Proving Lines Parallel 7. ANS: TOP: 3-6 Lines in the Coordinate Plane 8. ANS: m∠SUV = 72° TOP: 3-2 Angles Formed by Parallel Lines and Transversals 1 ID: A 9. ANS: The transversal is line m. The angles are alternate interior angles. TOP: 3-1 Lines and Angles MATCHING 10. 11. 12. 13. 14. ANS: ANS: ANS: ANS: ANS: B F G E C TOP: TOP: TOP: TOP: TOP: 3-1 Lines and Angles 3-1 Lines and Angles 3-1 Lines and Angles 3-1 Lines and Angles 3-1 Lines and Angles 15. 16. 17. 18. 19. 20. ANS: ANS: ANS: ANS: ANS: ANS: B F C D G H TOP: TOP: TOP: TOP: TOP: TOP: 3-6 Lines in the Coordinate Plane 3-4 Perpendicular Lines 3-5 Slopes of Lines 3-5 Slopes of Lines 3-6 Lines in the Coordinate Plane 3-5 Slopes of Lines 21. 22. 23. 24. 25. ANS: ANS: ANS: ANS: ANS: C E A B D TOP: TOP: TOP: TOP: TOP: 3-1 Lines and Angles 3-4 Perpendicular Lines 3-1 Lines and Angles 3-1 Lines and Angles 3-1 Lines and Angles 2