Chapt
Name:
Date:
er
Properties of Triangles
and Four-sided Figures
Practice 1
Classifying Triangles
Which of these triangles are equilateral, isosceles, or scalene?
Use a centimeter ruler to find out.
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1.
B
A
2.
D
E
F
C
Triangle ABC is a/an
Triangle DEF is a/an
triangle.
3.
triangle.
4.
L
P
Q
R
N
M
Triangle LMN is a/an
triangle.
Triangle PQR is a/an
triangle.
Lesson 13.1 Classifying Triangles
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Which of these triangles are right, obtuse, or acute?
Use a protractor to find out.
A
5.
6.
D
E
B
C
F
Triangle ABC is a/an
Triangle DEF is a/an
7.
M
triangle.
8.
P
L
R
Q
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triangle.
N
122
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Triangle LMN is a/an
Triangle PQR is a/an
triangle.
triangle.
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:42 AM
Name:
Date:
Practice 2
Measures of Angles of a Triangle
Complete.
1.
A
mA mB mC C
B
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2.
D
80°
80° 70° mF 70°
mF E
F
Measure the angles of the triangle. Then fill in the blanks.
3.
A
mA mB mC B
C
mA mB mC The sum of the angle measures in the triangle is
Lesson 13.2
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.
Measures of Angles of a Triangle
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These triangles are not drawn to scale. Find the unknown
angle measures.
4.
Find the measure of B.
5.
A
Find the measure of D.
D
43°
C
72°
E
50°
62°
B
6.
Find the measure of H.
7.
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F
Find the measure of QPS.
P
F
50°
15°
60°
H
R
32°
S
Q
26°
G
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:43 AM
Name:
Date:
Practice 3 Right, Isosceles, and Equilateral
Triangles
Complete. ABC and EFG are right triangles.
1.
B
mB A
mA mC © 2009 Marshall Cavendish International (Singapore) Private Limited
C
2.
E
F
mE mF mG G
Measure the angles of the triangle. Then fill in the blanks.
3.
mA A
mB mC C
mA m C B
These triangles are not drawn to scale. Identify and shade the right triangles.
4.
59°
70°
19°
65°
78°
25°
13°
90°
72°
Lesson 13.3 Right, Isosceles, and Equilateral Triangles
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These triangles are not drawn to scale. Find the unknown
angle measures.
Find the sum of the measures of A and B.
A
B
C
6.
Find the measure of C.
A
B
57°
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5.
C
7.
Find the measures of ADC and ABC.
A
28°
D
8.
C
Find the measures of EGF and DGE.
B
D
E
G
26°
F
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:45 AM
Name:
Date:
Complete. XYZ and PQR are isosceles triangles.
9.
Y
Which two sides are of equal length?
X
Which two angles have equal measures?
Z
10.
Q
Which two sides are of equal length?
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P
Which two angles have equal measures?
R
These triangles are not drawn to scale. Identify and shade
the isosceles triangles.
11.
64°
86°
52°
46°
75°
74°
80°
30°
80°
90°
Lesson 13.3 Right, Isosceles, and Equilateral Triangles
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These triangles are not drawn to scale. Find the unknown
angle measures.
12.
Find the measure of F.
13.
Find the measure of C.
E
D
A
53°
36°
F
C
Find the measure of TRS.
15.
Find the measure of d.
86°
R
X
W
U
20°
T
S
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14.
B
d
Z
Y
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:46 AM
Name:
Date:
Complete. Use your protractor and centimeter ruler to measure
the sides and angles. Which figure is an equilateral triangle?
Check the box.
16.
X
17.
A
C
B
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Z
Y
AB cm
XY cm
BC cm
YZ cm
AC cm
XZ cm
mA mX mB mY mC mZ Complete. ABC is an equilateral triangle.
A
C
18.
Which angles have measures equal
to the measure of A?
19.
Which sides have lengths equal to
the length of AB ?
20.
What can you say about the angles
of triangle ABC ?
B
Lesson 13.3 Right, Isosceles, and Equilateral Triangles
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These triangles are not drawn to scale. Identify and shade
the equilateral triangles.
21.
60°
40°
60°
60°
60°
These triangles are not drawn to scale. Find the unknown
angle measures.
22.
Find the measure of Q.
P
60°
R
23.
60°
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60°
Q
Find the measures of Y and Z.
X
60°
Z
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Y
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:47 AM
Name:
Date:
These triangles are not drawn to scale. Find the unknown
angle measures.
24.WX 5 XY 5 YW. Find the measure of d.
W
Z
X
d
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Y
25.
Find the measure of e.
L
O
M
e
N
26.Triangle PQR is an equilateral triangle. Triangle PST is an isosceles triangle.
The measures of a, b, and c are the same. Find the measure of d.
P
a bc
d
R
S
T
Q
Lesson 13.3 Right, Isosceles, and Equilateral Triangles
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1.
A teacher asked her students to sketch and label the angles of a triangle.
These are the angle measures that three students chose to draw.
Wayne: 120°, 80°, 10°
Ashley: 70°, 28°, 72°
Frank: 51°, 37°, 92°
Will each student be able to draw his or her triangle? Explain your answer.
Wayne:
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Ashley:
Frank:
2.
What are two ways to identify an isosceles triangle?
3.
Jordan is measuring the angles of a triangle.
He finds out that mA mB 60°.
Without measuring C, he says that
triangle ABC is an equilateral triangle.
Is he correct? Explain why.
132
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A
B
C
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:51 AM
Name:
Date:
Practice 4
Triangle Inequalities
Complete. Measure the sides of the triangle to the nearest half inch.
Then fill in the blanks.
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A
B
C
1.
AB in.
2.
BC 3.
AC in.
4.
AB BC in.
5.
BC AC 6.
AB AC in.
in.
in.
Use your answers in Exercises 4 to 6. Fill in the blanks with Yes or No.
7.
Is AB BC AC?
8.
Is BC AC AB ?
9.
Is AB AC BC ?
Lesson 13.4
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Triangle Inequalities
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Complete. Measure the sides of the triangle to the nearest centimeter.
Then fill in the blanks.
X
Z
10.
XY cm
11.
YZ 12.
XZ cm
13.
XY YZ cm
14.
YZ XZ 15.
XY XZ cm
cm
Use your answers in Exercises 10 to 15. Write the sides of the
triangle to make the inequalities true.
16.
XY YZ 17.
YZ XZ 18.
XY XZ 134
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cm
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Y
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:51 AM
Name:
Date:
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Show whether it is possible to form triangles with these lengths.
19.
6 in., 8 in., 12 in.
20.
9 in., 13 in., 3 in.
21.
2 cm, 4 cm, 7 cm
Lesson 13.4
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Triangle Inequalities
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The lengths of two sides of each triangle are given. Name a
possible length for the third side. The lengths are in whole
centimeters or whole inches.
A
22.
9 cm
?
AB is greater than 10 centimeters.
A possible length for AB is centimeters.
C
13 cm
P
QR is greater than 9 inches.
A possible length for QR is
inches.
8 in.
17 in.
Q
?
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23.
B
R
Solve.
24.
136
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I n the triangle EFG, EF 5 21 centimeters, FG 5 11 centimeters. The length of EG is in whole centimeters and is greater than 25 centimeters. What is a possible length of EG ?
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Chapter 13 Properties of Triangles and Four-sid
2/17/10 2:08:09 PM
Name:
Date:
Practice 5 Parallelogram, Rhombus, and Trapezoid
Complete. Figure ABCD is a parallelogram. Measure the sides and
angles of the figure.
B
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A
D
C
1.
AD cm
2.
AB cm
3.
BC cm
4.
DC cm
5.
mA 6.
mB 7.
mC 8.
mD 9.
Name the parallel sides of the figure.
10.
Name the opposite angles that are equal.
This parallelogram is not drawn to scale. Fill in the blanks.
11.
mQ m
P
Q
12.
mP 180° 13.
75
S
R
mR m
Lesson 13.5 Parallelogram, Rhombus, and Trapezoid
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These parallelograms are not drawn to scale.
Find the unknown angle measures.
15.
56
a
16.
61
f
135
17.
73
139
58
18.
x
19.
y
28°
g
b
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14.
p
62°
z
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:51 AM
Name:
Date:
Complete. Write the name of another side or angle of each rhombus.
20.
AB BC
A
21.
mB m
22.
mA m
B
D
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23.
S
UV 24.
mS m
25.
mT m
C
V
T
U
This rhombus is not drawn to scale. Fill in the blanks.
W
Z
X
53°
26.
mX m
27.
mW 28.
mY m
Y
Lesson 13.5 Parallelogram, Rhombus, and Trapezoid
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These rhombuses are not drawn to scale.
Find the unknown angle measures.
29.
30.
125°
57°
p
31.
32.
129°
52°
r
s
33.
34.
106°
45°
t
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q
v
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:52 AM
Name:
Date:
Measure the unknown angles. Then fill in the blanks.
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ABCD is a trapezoid where AB || DC.
35.
mA 36.
mB 37.
mC 38.
mD 39.
mA mD m
A
B
C
D
m
These trapezoids are not drawn to scale.
Find the unknown angle measures.
40.
AB || DC
A
41.
B
F
E
116°
D
EH || FG
C
H
58°
G
42.
JK || ML
43.
PS || QR
J
P
Q
97°
K
M
81°
109°
S
R
L
Lesson 13.5 Parallelogram, Rhombus, and Trapezoid
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These trapezoids are not drawn to scale.
Find the unknown angle measures.
TU || WV
T
45.
X
a
VW || YX
V
U
70°
c
40°
b
30°
85°
V
W
W
d
Y
46.
AB || DC
47.
EH || FG
F
B
A
24°
f
E
75°
D
X
70°
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44.
g
C
38°
H
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Chapter 13 Properties of Triangles and Four-si
2/25/09 2:02:57 AM
Name:
Date:
Put On Your Thinking Cap!
Challenging Practice
This figure is a rhombus and ADO CDO. Find the measure of DOC.
A
B
36°
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O
D
C
Chapter 13 Properties of Triangles and 4-sided Figures
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Put On Your Thinking Cap!
Problem Solving
1.
ABCD is a trapezoid in which AD || BC. Find the measure of CED.
B
62°
E
40°
D
C
2.
ABCD is a parallelogram and CDEF is a rhombus. Find the
measure of ADE.
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A
C
B
95°
A
D
F
E
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