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Name: ________________________ Class: ___________________ Date: __________ Parallel & Perpendicular Lines Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. The diagram below shows the construction of the perpendicular bisector of AB. Which statement is not true? a. AC = CB 1 b. CB = AB 2 c. AC = 2AB d. AC + CB = AB ____ 2. What is the slope of a line perpendicular to the line whose equation is 5x + 3y = 8? 5 a. 3 3 b. 5 3 c. − 5 5 d. − 3 1 ID: A Name: ________________________ ____ ID: A 3. Which graph could be used to find the solution to the following system of equations? y = −x + 2 y = x2 a. c. b. d. ← → ____ ← → 4. The diagram below illustrates the construction of PS parallel to RQ through point P. Which statement justifies this construction? a. m∠1 = m∠2 b. m∠1 = m∠3 c. PR ≅ RQ d. PS ≅ RQ 2 Name: ________________________ ID: A ____ 5. What is the equation of a line that passes through the point (−3,−11) and is parallel to the line whose equation is 2x − y = 4? a. y = 2x + 5 b. y = 2x − 5 1 25 c. y = x + 2 2 1 25 d. y = − x − 2 2 ____ 6. Find m∠ABC . a. b. c. d. ____ m∠ABC m∠ABC m∠ABC m∠ABC = 40º = 45º = 35º = 50º 7. Given the system of equations: y = x 2 − 4x x=4 The number of points of intersection is a. 1 b. 2 c. 3 d. 0 3 Name: ________________________ ____ ____ ID: A 2 8. What is the slope of a line perpendicular to the line whose equation is y = − x − 5 ? 3 3 a. − 2 2 b. − 3 2 c. 3 3 d. 2 9. The two lines represented by the equations below are graphed on a coordinate plane. x + 6y = 12 3(x − 2) = −y − 4 Which statement best describes the two lines? a. The lines are parallel. b. The lines are the same line. c. The lines are perpendicular. d. The lines intersect at an angle other than 90°. ____ 10. A transversal intersects two lines. Which condition would always make the two lines parallel? a. Vertical angles are congruent. b. Alternate interior angles are congruent. c. Corresponding angles are supplementary. d. Same-side interior angles are complementary. ____ 11. Find the slope of the line that contains (5, − 6) and (−1, − 4). 2 a. −5 b. −2 c. −3 d. −3 5 1 4 Name: ________________________ ID: A ____ 12. Based on the diagram below, which statement is true? a. b. c. d. a a b d Äb Äc Äc Äe Short Answer 13. Find an equation of the line passing through the point (5,4) and parallel to the line whose equation is 2x + y = 3. Answer:_________________________________ 5 Name: ________________________ ID: A 14. In the diagram below of quadrilateral ABCD with diagonal BD , m∠A = 93 , m∠ADB = 43 , m∠C = 3x + 5 , m∠BDC = x + 19 , and m∠DBC = 2x + 6 . Determine if AB is parallel to DC . Show your work and explain your reasoning. Answer:_________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ _______________________________________________________________________________________ 15. Solve the following system of equations graphically. 2x 2 − 4x = y + 1 x+y = 1 6 ID: A Parallel & Perpendicular Lines Unit Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 2 TOP: Constructions 2. ANS: B REF: fall0804ge STA: G.G.18 A 5 so the slope of this line is − Perpendicular lines have slope that 3 B are the opposite and reciprocal of each other. The slope of a line in standard form is − PTS: 2 3. ANS: C PTS: 4. ANS: TOP: 5. ANS: REF: fall0828ge 2 REF: fall0805ge A PTS: 2 Constructions B STA: G.G.62 TOP: Parallel and Perpendicular Lines STA: G.G.70 REF: fall0807ge TOP: Quadratic-Linear Systems STA: G.G.19 A −2 = 2. A parallel line would also The slope of a line in standard form is − , so the slope of this line is B −1 have a slope of 2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b −11 = 2(−3) + b −5 = b PTS: 2 REF: fall0812ge STA: G.G.65 1 TOP: Parallel and Perpendicular Lines ID: A 6. ANS: C (x)° = (3x − 70)° 0 = 2x − 70 70 = 2x 35 = x Corresponding angles are congruent. Subtract x from both sides. Add 70 to both sides. Divide both sides by 2. m∠ABC = 3x − 70 m∠ABC = 3(35) − 70 = 35° Substitute 35 for x. Simplify. Feedback A B C D If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Use the Corresponding Angles Postulate. Correct! First, set the measures of the corresponding angles equal to each other. Then, solve for x and substitute in the expression (3x - 70). PTS: 1 DIF: Advanced NAT: 8.3.3.g TOP: 7-2 Parallel and Perpendicular Lines 7. ANS: A STA: 8.G.4 y = x 2 − 4x = (4) 2 − 4(4) = 0 . (4,0) is the only intersection. PTS: 2 8. ANS: D REF: 060923ge STA: G.G.70 TOP: Quadratic-Linear Systems 2 2 The slope of y = − x − 5 is − . Perpendicular lines have slope that are opposite reciprocals. 3 3 PTS: 2 9. ANS: D x + 6y = 12 6y = −x + 12 1 y = − x+2 6 m=− REF: 080917ge STA: G.G.62 TOP: Parallel and Perpendicular Lines STA: G.G.63 REF: 061007ge TOP: Parallel and Perpendicular Lines STA: G.G.35 3(x − 2) = −y − 4 −3(x − 2) = y + 4 m = −3 1 6 PTS: 2 REF: 011119ge 10. ANS: B PTS: 2 TOP: Parallel Lines and Transversals 2 ID: A 11. ANS: C y2 − y1 m= x2 − x1 Use the slope formula. m= (−4) − (−6) (−1) − (5) Substitute (5, − 6) for (x 1 , y 1 ) and (−1, − 4) for (x 2 , y 2 ). m= 2 −6 Simplify. 1 = −3 Feedback A B C D Divide the difference in y-values by the difference in x-values. First, substitute the coordinates of the first point into (x1, x2) and the coordinates of the second point into (y1, y2) of the slope formula. Then, simplify. Correct! Use the slope formula. PTS: 1 DIF: Basic REF: Page 320 OBJ: 5-4.1 Finding Slope by Using the Slope Formula NAT: 12.5.2.b STA: A.A.33 TOP: 5-4 The Slope Formula 12. ANS: D The marked 60º angle and the angle above it are on the same straight line and supplementary. This unmarked supplementary angle is 120º. Because the unmarked 120º angle and the marked 120º angle are alternate exterior angles and congruent, d Ä e. PTS: 2 REF: 080901ge STA: G.G.35 TOP: Parallel Lines and Transversals SHORT ANSWER 13. ANS: y = −2x + 14 . The slope of 2x + y = 3 is −A −2 = = −2. y = mx + b . B 1 4 = (−2)(5) + b b = 14 PTS: 2 REF: 060931ge STA: G.G.65 TOP: Parallel and Perpendicular Lines 14. ANS: Yes, m∠ABD = m∠BDC = 44 180 − (93 + 43) = 44 x + 19 + 2x + 6 + 3x + 5 = 180 . Because alternate interior 6x + 30 = 180 6x = 150 x = 25 x + 19 = 44 angles ∠ABD and ∠CDB are congruent, AB is parallel to DC . PTS: 4 REF: 081035ge STA: G.G.35 3 TOP: Parallel Lines and Transversals ID: A 15. ANS: PTS: 4 REF: 061137ge STA: G.G.70 4 TOP: Quadratic-Linear Systems