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Name _________________________________________ CHAPTER 3 1. a. Explain how to show that the given lines are parallel by using angles. Then show that the lines are parallel by using this method. b. Explain how to show that the given lines are parallel by using the equations of the two lines. Then show that the lines are parallel by using this method. c. Explain how to find the distance between the given lines. 2. The figure at the right shows the front view of a cellular phone tower’s structure. a. Identify all pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles formed by lines m, n, and p. b. Suppose that lines m and n are parallel. Identify all congruent angles formed by lines m, n, and p. c. Suppose that lines m and n are parallel and that m 1 = 46° and m 6 = (2x)º. Find the value of x. d. Suppose that m 3 = 112° and m 7 = (4x)°. Find the value of x that makes m n . e. The graph models the total cost of cellular phone service from two companies for several months. Write an equation of each line. Tell what the slope and y-intercept mean in this situation. Date ____________________ Name _________________________________________ CHAPTER 3 Date ____________________ Alternative Assessment and Rubric continued For use after the chapter "Parallel and Perpendicular Lines” Journal Solution 1. Complete answers should include: a. an explanation that a transversal should be drawn on the graph and that one of the following postulates or theorems should be used along with measuring the appropriate angles to determine whether the lines are parallel: Corresponding Angles Converse, Alternate Interior Angles Converse, Alternate Exterior Angles Converse, Consecutive Interior Angles Converse; a solution that shows a transversal drawn on the graph, the measures of the appropriate angles, a statement of the theorem or postulate that was used in the conclusion. b. an explanation that the slopes of the lines should be determined and compared; a solution that shows the slopes of both lines as 4, and the conclusion that because the slopes are equal, the lines are parallel. c. an explanation that the length of a perpendicular segment from one line to the other should be found by using the distance formula. Multi-Step Problem Solution 2. a. corresponding angles: 1 and 5, 2 and 6, 3 and 7, 4 and 8; alternate interior angles: 3 and 6, 4 and 5; alternate exterior angles: 1 and 8, 2 and 7; consecutive interior angles: 3 and 5, 4 and 6 b. 1, 4, 5, and 8; 2, 3, 6, and 7 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. c. 67 d. 28 e. y = 50x + 25; y = 40x + 50; The slope is the amount of money paid each month and the y-intercept is the initial cost of the service. f. Sample answer: Company 2, because it appears to cost less as time goes on. Other factors might include how many free minutes the plan includes and whether the plan includes a free phone or not. Multi-Step Problem Rubric 4 The student answers all parts of the problem correctly and completely. The student shows all work. The student’s work is neat. 3 The student answers all parts of the problem. The student’s work may have one or two errors in the identification of pair of angles, the calculation of angle measures, or in the calculation of the equations of the lines. The student shows most work. The student’s work is neat. 2 The student answers all parts of the problem. The student’s work contains multiple errors, but the student shows most work. The student’s work is sloppy. 1 The student does not complete all parts of the problem. The work contains many errors in logic. The student’s work is sloppy, or no work is shown. Geometry Assessment Book Answers for Parallel and Perpendicular Lines Alternative Assessment 1. a. Sample answer: Let the y-axis be the transversal that cuts the lines in the graph. The lines are parallel by the Corresponding Angles Converse because m ABC = m BDE = 14°. b. Find the slopes of the lines. If they are the same, then the lines are parallel. The slopes of the given lines are both 4, so the lines are parallel. c. Use the distance formula to find the length of a perpendicular segment that connects the two lines. 2. a. corresponding angles: 1 and 5, 2 and 6, 3 and 7, 4 and 8; alternate interior angles: 3 and 6, 4 and 5; alternate exterior angles: 1 and 8, 2 and 7; consecutive interior angles: 3 and 5, 4 and 6 b. 1, 4, 5, and 8; 2, 3, 6, and 7 c. 67 d. 28 e. y = 50x + 25; y = 40x + 50; The slope is the amount of money paid each month and the y-intercept is the initial cost of the service. f. Sample answer: Company 2, because it appears to cost less as time goes on. Other factors might include how many free minutes the plan includes and whether the plan includes a free phone or not. Geometry Assessment Book