Date: P
H A TE
13
R
C
Name:
Properties of Triangles
and Four-Sided Figures
Worksheet 1
Classifying Triangles
The figures are not drawn to scale.
Write true or false for each statement.
Triangle ABC is an equilateral triangle.
A
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C
B
1.
Any two sides are equal.
2.
All the angles measure 60°.
3.
A right triangle can also be an equilateral triangle.
4.
An equilateral triangle can also be an isosceles triangle.
5.
An isosceles triangle can never be an equilateral triangle.
Put a check in the box if the triangle is an equilateral triangle.
6.
7.
60°
60°
60°
30°
8.
45°
45°
Reteach 5B
153
Name:
Date: Write true or false for each statement.
Triangle PQR is an isosceles triangle.
P
Q
30°
30°
R
9.
Two sides are equal.
10.
Any two angles are equal.
11.
A triangle with three equal sides can also be an isosceles triangle. 12.
A right triangle can also be an isosceles triangle. Put a check in the box if the triangle is an isosceles triangle.
14.
52°
52°
15.
34°
W
X
16.
All three sides are of different lengths.
17.
All three angle measures are different.
Chapter 13
72°
112°
Write true or false for each statement.
Triangle WXY is a scalene triangle.
154
46°
Lesson 13.1
Y
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13.
Name:
Date: Put a check in the box if the triangle is a scalene triangle.
18.
19.
20.
Write true or false for each statement.
A
Triangle ABC is a right triangle.
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B
C
21.
One angle is 90°. 22.
The sum of any two angle measures is 90°. 23.
The sum of all the angle measures is 90°. Put a check in the box if the triangle is a right triangle.
24.
25.
38°
52°
26.
27°
72°
19°
Reteach 5B
155
Name:
Date: Write true or false for each statement.
Triangle STU is an obtuse triangle.
S
T
U
27.
All the angles measure less than 90°.
28.
An obtuse triangle can also be an isosceles or a scalene triangle.
Put a check in the box if the triangle is an obtuse triangle.
30.
31.
Write true or false for each statement.
Triangle PQR is an acute triangle.
Q
32.
All the angles measure greater than 90°.
33.
An acute triangle can also be an equilateral,
isosceles, or scalene triangle.
P
R
Put a check in the box if the triangle is an acute triangle.
34.
156
35.
Chapter 13
Lesson 13.1
36.
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29.
Name:
Date: Worksheet 2
Measures of Angles of a Triangle
The figures are not drawn to scale.
Write true or false for each statement.
Triangle XYZ has three unequal sides.
Z
Y
X
1.
X, Y, and Z are the three angles of the triangle. 2.
The sum of the measures of X, Y, and Z is 180°. 3.
All the angles must measure less than 90°. 4.
At most one angle measure is equal to or greater than 90°. Complete. Find the unknown angle measures.
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Example
A
78°
B
26°
C
mB 5
76˚
Reteach 5B
157
Name:
Date: 5.
X
82°
Z
36°
mY 5
Y
6.
L 23°
N
47°
mM 5
M
7.
U
T
108°
35°
mT 5
S
8.
​
PR ​
​ is a line segment. Find the measure of PQS.
38°
P
9.
78°
27°
​
AC ​
​ is a line segment. Find the measure of BDC.
A
B
53°
69°
D
158
R
S
Chapter 13
Lesson 13.2
26°
C
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Q
Name:
10.
Date: ABC is a right triangle.
B
D
A
a.
C
Find the measure of C.
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​
​

​ at D. Find the measure of DAC.
b.​AD ​is perpendicular to BC ​
Reteach 5B
159
Name:
Date: Complete.
A
11.
B
m
C
1 m
D
1 m
 180°
Write true or false for each statement.
A
C
12.
mABC 1 mBAC 1 mBCA  90°
13.
mADC 1 mDAC 1 mBAC 1 mABC  180°
14.
mADC 1 mDAC 1 mACD  180°
160
Chapter 13
Lesson 13.2
D
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B
Name:
Date: Use the figure below to complete Exercises 15 to 18.
Q
R
P
S
Write 3 sets of angles that total 180°.
15.
m
m
m
16.
m
m
m
17.
m
m
m
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Write a set of 4 angles that total 180°.
18.
m
m
m
m
Reteach 5B
161
Name:
Date: Triangle ABC is not drawn to scale.
A
B
C
Write true or false for each statement.
19.
If mB  mC  90°, then mA is 90°.
20.
If mA  90°, then mB is less than 90°.
21.
If mA  80°, then mB 
mC 
22.
If mA  80°, then mB 
mC 
23.
If mA  80°, then mB 
mC 
162
Chapter 13
Lesson 13.2
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Write 3 different possible measures for B and C.
Name:
Date: Worksheet 3 Right, Isosceles, and Equilateral Triangles
Find the unknown angle measure in each right triangle.
Example
x
This is a right triangle.
56°
mx 5
1.
34
°
2.
68°
z
65°
y
my 5
°
mz 5
°
Find the unknown angle measure in each isosceles triangle.
Example
This is an isosceles triangle.
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p
70°
mp 5
40°
70
3.
°
4.
q
r
65°
45°
mq 5
°
mr 5
°
Reteach 5B
163
Name:
Date: Find the unknown angle measure(s) in each isosceles triangle.
Example
L
M
55°
N
5.
55
°
mLNM 5
70
°
E
78°
F
6.
mMLN 5
G
mFEG 5
°
mEFG 5
°
​
​ is a ray.
PS ​
Q
m
R
128°
S
7.
mm 5
°
mn 5
°
​
AC ​
​ is a ray.
A
50°
B
n 38°
E
164
Chapter 13
D
Lesson 13.3
C
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P
Name:
8.
Date: ABC is an isosceles triangle with sides AB 5 AC.
a. mA 5 70°
Find the measure of C.
​
​
​ is perpendicular to BC ​
​ .
Point D is on segment BC. AD ​
Find the measure of DAC.
b.
9.
ABC is an isosceles triangle with sides AB 5 AC.
a. mA 5 105°
Find the measure of C.
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b.
Point D is on segment BC.
mDAC 5 25°
Find the measure of ADB.
Find the unknown angle measure(s).
Example
This is an equilateral triangle.
60°
a
60°
ma 5 60°
Reteach 5B
165
Name:
Date: 10.
11.
c
60°
b
12.
13.
e
g
60°
d
f
14.
15.
52°
i
j
16.
17.
66°
24°
61°
53°
k
166
Chapter 13
Lesson 13.3
l
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h
128°
Name:
Date: Worksheet 4
Triangle Inequalities
The figure is not drawn to scale.
Example
Complete.
W
6 cm
X
4 cm
Y
4
WX 5
6
cm
XY 5
WY 5
6
cm
WX 1 XY 5
XY 1 WY 5
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6 cm
10
cm
cm
10
cm
12
WX 1 WY 5
cm
Look at the triangle WXY. Fill in the blanks with Yes or No.
Is WX 1 XY  WY ?
Yes
Is XY 1 WY  WX ?
Yes
Is WX 1 WY  XY ?
Yes
These are inequalities.
Reteach 5B
167
Name:
Date: The figure is not drawn to scale.
Complete.
P
3 in.
5 in.
R
7 in.
1.
PQ 5
in.
2.
QR 5
in.
3.
PR 5
in.
4.
PQ 1 QR 5
in.
5.
QR 1 PR 5
in.
6.
PQ 1 PR 5
in.
Look at the triangle PQR. Fill in the blanks with Yes or No.
7.
Is PQ 1 QR  PR?
8.
Is QR 1 PR  PQ?
9.
Is PQ 1 PR  QR?
168
Chapter 13
Lesson 13.4
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Q
Name:
Date: © Marshall Cavendish International (Singapore) Private Limited.
Show whether it is possible to form triangles with these sides.
10.
2 in., 3 in., 5 in.
11.
4 cm, 5 cm, 10 cm
12.
6 cm, 7 cm, 8 cm
Reteach 5B
169
Name:
Date: Find all the possible lengths for the missing side. The lengths are
in whole centimeters or whole inches.
Example
D
DF is greater than 4 centimeters.
​
What are the possible lengths of DF
​ ​?
4 cm
F
3 cm
E
DE 1 EF 5 4 cm 1 3 cm
5 7 cm
DE 1 EF  DF
7 cm  DF
13.
In triangle ABC, AB 5 5 inches, BC 5 6 inches,
and AC is greater than
​

4 inches. What are the possible lengths of AC ​ ​ ?
14.
XYZ is a triangle in which XY 5 11 centimeters and YZ 5 15 centimeters.
and is greater than 20 centimeters.
The length of XZ is in whole centimeters
​

What are the possible lengths of XZ ​ ​ ?
170
Chapter 13
Lesson 13.4
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So, DF is greater than 4 centimeters and less
than 7 centimeters. The possible lengths of DF
are 5 centimeters and 6 centimeters.