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Geometry Name: ____________________________________ Date: ____________________ Period: ________ Chapter 3 Test Review Short Answer In questions 1 - 4, use the following diagram. In questions 5 and 6, use the following figure. 5. What is the value of x? 1. What is the angle relationship between ∠3 and ∠6? 6. What is the measure of the obtuse angle? 2. What pair of angles are corresponding angles? 7. If two angles lie between two lines and on opposite sides of a transversal, then the angles are ________________________. 3. What is the angle relationship between ∠4 and ∠6? 4. What pair of angles are alternate exterior angles? 8. Which pair of angles are corresponding angles? 1 9. If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are ___________________. 12. What is m∠1 in the figure below? 10. What is one way to describe the vertical bars of a football goalpost? 13. Based on the diagram, which theorem would you use to support the statement m∠A + m∠B = 180o? 11. What value of x makes m || n? 14. Find m∠1. 2 15. Which lines are parallel in the figure below? ← → ← → 18. Find x if CD ⊥ FG . 16. Find x and y. 19. What best describes the relationship between line 6x - 2y = 1 and line x + 3y = 12? 20. Write an equation of the line with slope = -2 and y-intercept = 5. 17. What value must x be in order to conclude Q || R? 21. What is the equation of the line through the point (2, 1) and perpendicular to the line through (-4, 1) and (3, -2)? 22. What is the equation of the line that passes through the point (-3, 5) with a slope of 4? 3 23. Find the slope of a ladder placed 4 feet from the wall touching the wall at a height of 12 feet. 25. What is the equation of the line passing through the point (4, 1) that is parallel to the line with the equation 6x - 3y = 21? 24. Describe the slope of the line passing through the points A(-2, 3) and B(4, -3) 26. Describe the lines passing through the given points. (parallel, perpendicular, or neither) Line 1: (5, 8), (4, 3) Line 2: (-4, 9), (-2, -1) Other ← → ← → 27. Given: QS ⊥ PR Prove: m∠PTS = 90° 28. Write a proof. Given: l ⊥ n, m ⊥ n Prove: ∠3 and ∠6 are supplementary 4 ID: A Chapter 3 Test Review Answer Section SHORT ANSWER 1. ANS: The angles are consecutive interior angles. PTS: 1 2. ANS: ∠1 and ∠5 PTS: 1 3. ANS: The angles are alternate interior angles. PTS: 1 4. ANS: ∠1 and ∠7 PTS: 1 5. ANS: 18 PTS: 1 6. ANS: 130o PTS: 1 7. ANS: alternate interior angles PTS: 1 8. ANS: ∠3 and ∠7 PTS: 1 9. ANS: parallel PTS: 1 1 ID: A 10. ANS: parallel PTS: 1 11. ANS: 20 PTS: 1 12. ANS: 28o PTS: 1 13. ANS: Consecutive Interior Angles Theorem PTS: 1 14. ANS: 56o PTS: 1 15. ANS: p and q PTS: 1 16. ANS: x = 8, y = 11 PTS: 1 17. ANS: 36 PTS: 1 18. ANS: 15 PTS: 1 19. ANS: perpendicular PTS: 1 20. ANS: y = -2x + 5 PTS: 1 2 ID: A 21. ANS: 7 11 y = x− 3 3 PTS: 1 22. ANS: y = 4x + 17 PTS: 1 23. ANS: 3 PTS: 1 24. ANS: negative PTS: 1 25. ANS: y = 2x - 7 PTS: 1 26. ANS: neither PTS: 1 OTHER 27. ANS: Statements ← → Reasons ← → 1. QS ⊥ PR 1. Given 2. ∠PTS is a right ∠ 2. Definition of perpendicular lines 3. m∠PTS = 90 o 3. Definition of a right angle PTS: 1 NAT: NCTM 9-12.REA.3 | NCTM 9-12.REA.4 | NCTM 9-12.GEO.1.c KEY: angle | right | perpendicular | proof BLM: Analysis NOT: 978-0-618-65613-4 3 ID: A 28. ANS: Statements Reasons 1. l ⊥ n, m ⊥ n 1. Given 2. l m 2. Lines Perpendicular to a Transversal Theorem 3. ∠1 and ∠3 are supplementary 3. Linear Pair Postulate 4. m∠1 + m∠3 = 180o 4. Defintion of supplementary 5. ∠1 ≅ ∠6 5. Alternate Exterior Angles Theorem 6. m∠1 = m∠6 6. Def. of congruent angles 7. m∠6 + m∠3 = 180o 7. Substitution 8. ∠6 and ∠3 are supplementary 8. Def. of suppl. PTS: 1 NAT: NCTM 9-12.GEO.1.c | NCTM 9-12.REA.3 | NCTM 9-12.REA.4 KEY: perpendicular | supplementary | proof BLM: Analysis NOT: 978-0-618-65613-4 4