Download Parallel Lines and Triangles

Name
Class
Date
Practice
3-5
Form G
Parallel Lines and Triangles
Find ml1.
1.
92
25
1
1 73
2. 20
3.
87
63
60
80
40
1
Algebra Find the value of each variable.
4.
28
17
67; 113; 50
5.
x
y z 57
6.
59; 81; 99
13
y
x
40
85 x y z
z
33; 134; 46
24
7. Use the diagram at the right to answer the questions.
a. Which angle is an exterior angle? l1
50
84
38
b. What are its remote interior angles?
l1 has the remote interior angle measurements of 70 and 38.
c. Find m/1 and m/2.
ml1 5 108; ml2 5 72
70
2 1
Find the value of the variables and the measures of the angles.
8.
(8x 2)
9.
5; 42; 48
36, 78; 66
x
(9x 3)
(2x 6)
C
10. In the figure at the right, ED ' CB and
ED bisects /CDB. Find m/DBA. 108
(2x 6)
(2x)
E
D
12 x ? B
A
11. Reasoning What is the measure of each angle in an isosceles right
triangle? Explain. 45, 45, 90; Sample: because the triangle is isosceles, two sides are
equal measure. So two angles are equal measure and one angle is 908, since the
triangle is right and 45 1 45 1 90 5 180.
12. The ratio of the angle measures of the acute angles in a right triangle is 2 i 3.
Find the measures of the acute angles.
36 and 54
Prentice Hall Gold Geometry • Teaching Resources
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Name
Class
Date
Practice (continued)
3-5
Form G
Parallel Lines and Triangles
13. Paragraph Proof Prove that the sum of the exterior angles of a triangle
is always 3608.
1 C
2
Given: nABC
Prove: m/1 1 m/4 1 m/6 5 360
Sample: The sum of the interior angles of a triangle is 180, so
A 3
ml2 1 ml3 1 ml5 5 180. Because l1 and l2, l3 and l4, l5
4
and l6 are linear pairs, the sum of the measures of each pair is 180.
So, ml1 1 ml2 1 ml3 1 ml4 1 ml5 1 ml6 5 540. Using the
Substitution Property of Equality, ml1 1 ml4 1 ml6 1 180 5 540.
Then, by the Subtraction Property of Equality, ml1 1 ml4 1 ml6 5 360.
5 6
B
14. A ramp built for wheelchairs is shown below.
82
R
a. Find the measures of the remote interior angles for /R. 90; 82
b. Find m/R. 172
A
15. Error Analysis A student draws a diagram of nABC with angle
)
bisector AD as shown, and says that the measure of /CAD must be 308.
A
a. What is the student’s error in reasoning?
51
51
The triangle might not be an equilateral triangle.
72
86
17.
70
3
4
B
B
D
Find each missing angle measure.
16.
D
C
b. Draw a diagram that would show an alternate answer.
Answers may vary. Sample shown at the right.
C
38
31
5
116
ml3 5 22; ml4 5 22; ml5 5 88
1
2
ml1 5 33; ml2 5 52
18. Reasoning Two angles of a triangle measure 53 and 39. What is the measure
of the largest exterior angle of the triangle? Explain.
141; answers may vary. Sample: If two angles are 53 and 39, the third angle
will be 88. The measure of the largest exterior angle will be the sum of the two
larger angles, and 53 1 88 5 141.
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
44