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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
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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