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Name: ________________________ Class: ___________________ Date: __________ Geometry - Chapter 3 Review 15-16 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. Identify a pair of parallel segments. a. AB Ä EH c. AB Ä HG b. FB Ä AB d. DH Ä FG 2. Use the Converse of the Corresponding Angles Postulate and ∠1 ≅ ∠2 to show that l Ä m. a. b. c. d. ∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are corresponding angles. So by the Converse of the Corresponding Angles Postulate, l Ä m. ∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are alternate interior angles. So by the Converse of the Alternate Interior Angles Postulate, l Ä m. By the Converse of the Corresponding Angles Postulate, ∠1 ≅ ∠2. From the diagram, l Ä m. ∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are corresponding angles. So by the Corresponding Angles Postulate, l Ä m. 1 ID: A Name: ________________________ ID: A Short Answer 3. Give an example of corresponding angles. 4. Find m∠RST . 5. Find m∠1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.) 2 Name: ________________________ ID: A 6. Use the slope formula to determine the slope of the line. Show your work. NO work, NO credit. 7. Graph the line y − 3 = 4(x − 6) . 3 Name: ________________________ ID: A 8. Write a two-column proof. Given: m∠1 + m∠2 = 180° Prove: l Ä m Complete the proof. Proof: Statements 1. m∠1 + m∠2 = 180° 2. m∠1 = m∠3 3. m∠3 + m∠2 = 180° 4. l Ä m Reasons 1. Given 2. [1] 3. Substitution (Steps 1 and 2) 4. [2] 9. Write and solve an inequality for x. 10. Find m∠1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.) 4 Name: ________________________ ID: A 11. Write a two-column proof. Given: t ⊥ l, ∠1 ≅ ∠2 Prove: m Ä l Complete the proof. Proof: Statements 1. [1] 2. t ⊥ m 3. m Ä l Reasons 1. Given 2. [2] 3. [3] 12. AB Ä CD for A(4, − 5), B(−2, − 3) , C(x, − 2), and D(6, y) . Find a set of possible values for x and y. Matching 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 ____ 13. lines that are not coplanar ____ 14. planes that do not intersect ____ 15. lines that intersect at 90° angles ____ 16. a line perpendicular to a segment at the segment’s midpoint ____ 17. lines in the same plane that do not intersect 5 Name: ________________________ ID: A 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 ____ 18. a line that intersects two coplanar lines at two different points ____ 19. 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 ____ 20. 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 ____ 21. 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 ____ 22. 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 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 ____ 23. y − y 1 = m(x − x 1 ) , where m is the slope and (x 1 , y 1 ) is a point on the line ____ 24. the difference in the y-values of two points on a line ____ 25. a line with slope m and y-intercept b can be written in the form y = mx + b ____ 26. a measure of the steepness of a line ____ 27. the length of the perpendicular segment from the point to the line ____ 28. the difference in the x-values of two points on a line 6 ID: A Geometry - Chapter 3 Review 15-16 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A TOP: 3-1 Lines and Angles TOP: 3-3 Proving Lines Parallel SHORT ANSWER 3. ANS: ∠8 and ∠4 TOP: 3-1 Lines and Angles 4. ANS: m∠RST = 72° TOP: 3-2 Angles Formed by Parallel Lines and Transversals 5. ANS: m∠1 = 135° TOP: 3-4 Perpendicular Lines 6. ANS: −2 TOP: 3-5 Slopes of Lines 7. ANS: TOP: 3-6 Lines in the Coordinate Plane 1 ID: A 8. ANS: [1] Vertical Angle Theorem [2] Converse of the Same-Side Interior Angles Theorem TOP: 3-3 Proving Lines Parallel 9. ANS: x>2 TOP: 3-4 Perpendicular Lines 10. ANS: m∠1 = 85° TOP: 3-2 Angles Formed by Parallel Lines and Transversals 11. ANS: [1] t ⊥ l, ∠1 ≅ ∠2 [2] 2 intersecting lines form linear pair of ≅ ∠s → lines ⊥. [3] 2 lines ⊥ to the same line → lines Ä. TOP: 3-4 Perpendicular Lines 12. ANS: ÏÔÔ ¸ÔÔ | 1 ÌÔ ÊÁË x, y ˆ˜¯ | y = 3 x − 4 , x ≠ 6 ˝Ô ÔÓ Ô˛ TOP: 3-5 Slopes of Lines MATCHING 13. 14. 15. 16. 17. ANS: ANS: ANS: ANS: ANS: D B C E A TOP: TOP: TOP: TOP: TOP: 3-1 Lines and Angles 3-1 Lines and Angles 3-1 Lines and Angles 3-4 Perpendicular Lines 3-1 Lines and Angles 18. 19. 20. 21. 22. ANS: ANS: ANS: ANS: ANS: E C G B F 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 23. 24. 25. 26. 27. 28. ANS: ANS: ANS: ANS: ANS: ANS: B C G H F D TOP: TOP: TOP: TOP: TOP: TOP: 3-6 Lines in the Coordinate Plane 3-5 Slopes of Lines 3-6 Lines in the Coordinate Plane 3-5 Slopes of Lines 3-4 Perpendicular Lines 3-5 Slopes of Lines 2