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NAME _____________________________________________ DATE __________________ PERIOD _________
Test, Form 3B
SCORE _________
For Exercises 1 and 2, write and solve an equation to find each
missing length. Round to the nearest tenth if necessary.
1. An observer is standing 20 feet
from a tree with a hanging
birdhouse. She is looking at the
birdhouse. How far from the ground
is the birdhouse? Round to the
nearest tenth if necessary.
25 ft
x
20 ft
2. Kenneth wants to wrap a collapsible fishing
rod in the box shown at the right. Find the
length of the diagonal of the box. Round to the
nearest tenth if necessary.
x2 + 202 =
2
1. 25 ; 15 ft
x in.
18 in.
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
10 in.
102 + 182 =
2
2. x ; 20.6 in
For Exercises 3 and 4, find the distance between each pair of
points with the given coordinates. Round to the nearest tenth if
necessary.
3. (4.25, 5.5), (3.5, 0)
3. 5.6 units
4. (-2, 4), (-5, -2)
4. 6.7 units
Find the value of x in each figure.
5.
x°
(x°+14°)
62°
6.
5.
24
6.
48
(x + 35)°
(2x + 1)°
7. A shelf is in the shape of a triangle. Find the angles of the triangle if
the measures of the angles are in the ratio x : x : 4x.
7. 30°, 30°, 120°
119
Course 3 • Chapter 5 Triangles and the Pythagorean Theorem
P rinter P DF
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NAME _____________________________________________ DATE __________________ PERIOD _________
Test, Form 3B
SCORE _________
(continued)
Sample answer:
They are all 60˚.
8. What is true about the angles in an equilateral triangle?
8.
9. What is the perimeter of the triangle?
x in.
3 in.
9.
4 in.
10. Find the measure of an exterior angle of a regular decagon.
10.
11. Find the sum of the measures of the interior angles of a 50-gon.
11.
12. The side view of a house (the “side elevation”) is often in the shape of
a pentagon. If the angle at the roof is 150° and there are two other
angles of 90°, what is the sum of the measures of the other two
12.
angles?
14. Use the proof to find the missing reason.
Given: two parallel lines cut by a
transversal, m∠5 = 4x, and
m∠7 = 96°
Prove: x = 24
Proof:
Statements
1. m∠5 = 4x, m∠7 = 96°
2. m∠5 = m∠7
3. 4x = 96
4. x = 24
120
Reasons
Given
?
Substitution
Division Property
1 2
8 7
36˚
8,640˚
210˚
Yes; 102 + 242
= 262
13.
3 4
6 5
Corresponding
angles have
14. equal measures.
Course 3 • Chapter 5 Triangles and the Pythagorean Theorem
P rinter P DF
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
13. A triangle has side lengths of 10 inches, 24 inches, and 26 inches. Is
the triangle a right triangle? Explain.
12 in.