NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Lesson Reading Guide
Congruent Polygons
Get Ready for the Lesson
Read the introduction at the top of page 320 in your textbook.
Write your answers below.
1. How many different rectangles are used in the painting? Draw each
rectangle.
Read the Lesson
3. What does it mean for two angles to be congruent?
4. What does it mean for two polygons to be congruent?
Lesson 6–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Copy the painting and label all matching rectangles with the same
number, starting with 1.
5. What does congruence mean in your own words?
Remember What You Learned
6. Make a simple drawing of the front of a house. Include at least two pairs
of congruent polygons in your drawing. Then write a sentence describing
the congruent polygons.
Chapter 6
25
Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Study Guide and Intervention
Congruent Polygons
Two polygons are congruent if all pairs of corresponding angles are congruent and all pairs of
corresponding sides are congruent. The letters identifying each polygon are written so that
corresponding vertices appear in the same order.
Example 1
Determine whether the triangles
shown are congruent. If so, name
the corresponding parts and write
a congruence statement.
Angles The arcs indicate that A D, B F, and
C E.
Sides The side measures indicate that AB
DF
,
BC
FE
, and C
A
ED
.
B
0.8 cm
2 cm
D
C
2 cm
1.5 cm
1.5 cm
E 0.8 cm
F
A
Since all pairs of corresponding sides and angles are congruent, the two triangles are
congruent. One congruence statement is ABC DFE.
In the figure, MNB LJH.
2.6 cm
M
N
30˚
a. Find LJ.
MN
corresponds to LJ
So, M
N
.
LJ
Since MN 2.6 centimeters, LJ 2.6 centimeters.
H
3 cm
1.5 cm
60˚
B
b. Find mH.
According to the congruence statement, B and H are
corresponding angles. So, B H. Since mB 60°,
mH 60°.
J
L
Exercises
Determine whether the polygons shown are congruent. If so, name
the corresponding parts and write a congruence statement.
1.
P
G
4m
3m
6m
H
6m
R
3m
4m
S
M
G
50˚
In the figure, GFD TRE.
Find each measure.
2. mR
E
20 ft
100˚ F
45 ft
3. RT
37 ft
R
30˚
4. mE
D
Chapter 6
26
T
Course 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Examples
NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Skills Practice
Congruent Polygons
Determine whether the polygons shown are congruent. If so, name the
corresponding parts and write a congruence statement.
2.
R
22 m
C
35 m
22 m
35 m
C 140˚ D
W
140˚
N
40˚
D
F
A
3 in.
4 in.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
E
5.
B
P
38˚
9. mK
45˚
D
X 24 m Y
70˚
B 120˚
5 in.
28.8 m
5 in.
A
20 m R
S
120˚
80˚
Z
C
D
80˚
R 70˚
T
U
E
In the figure, HFI MLK. Find each measure.
7. mM
35˚
M
6.
F
24 m
4 in.
100˚
O
C
3 in.
S
R
100˚
N
P
V
4.
45˚ L
35˚
142˚
142˚
E
29 m
3.
38˚
40˚
29 m
B
M
L
H
8. ML
10 yd 30˚
7 yd
40˚
10. KM
F
K
110˚
6 yd I
M
In the figure, quadrilateral ACDB quadrilateral EFGH. Find each measure.
11. mH
12. EF
A
28 ft
60˚
13. mF
14. HG
C
Chapter 6
120˚
38 ft
27
H
G
B
20 ft
75˚
105˚
D
E
F
25 ft
Course 3
Lesson 6–4
1.
NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Practice
Congruent Polygons
Determine whether the polygons are congruent. If so, name the corresponding
parts and write a congruence statement.
1.
12 mm S
Y
13 mm
5 cm
T
4 cm
A 2 cm C
13 mm
X
12 mm
4 cm
5 cm
2. R
F 2 cm D
B
Z
E
3. P
Q
X
W
4.
25 in.
J
K
F
10 in.
8 in.
G
L
M
20 in.
S
R
Z
Y
H
In the figure, ABC DEF. Find each measure.
5. DF
7. mD
A
6. DE
8. mE
8m
45˚
80˚
F
B
10 m
D
C E
In the figure, quadrilateral PQRS is congruent to
quadrilateral TUVW. Find each measure.
9. PQ
11. mU
18 cm U
V
R
10. QR
12. mV
70˚
50˚
Q
13. FLAGS The two flags flying on the
pole are in the shape of triangles.
If FGH KLM, mF = 80,
and mH = 80, find mL.
27 cm
S
W
P
T
14. FLOORING Tevin designed custom
tiles for his shower as shown. The tiles
are congruent quadrilaterals. Write a
congruence statement. Then find mJ if
mA = 90, mB = 60, and mD = 90.
F
G
B J
A
H
K
D
L
CM
K
L
M
Chapter 6
28
Course 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
I
NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Word Problem Practice
Congruent Polygons
D
10 m
A
3m
B 9m C
AIRPLANES The diagram at the right is of an airplane
120°
E
110°
F
G
80°
1. Name an unlabeled wing part whose
length is 3 meters. Explain your
answer.
2. Explain how a quality control person
could find out if mDCB was correct.
3. WHALES The flukes of the Beluga
whale are shaped like triangles.
Determine whether these triangles are
congruent. If so, name the
corresponding parts and write a
congruence statement. (Hint: RQ
is a
side of each triangle.)
4. PATTERNS Mandy is making name tags
in the shape of triangles. They all
should be the same size. Explain how
she can use a pattern to make 25 name
tags. How does she know they are all
congruent?
P
R
Q
S
5. ALGEBRA Find the value of x in the two
congruent triangles.
6. NATURE Part of a spider’s web is shown
in the figure. Determine whether the
two marked triangles are congruent. If
so, name the corresponding parts and
write a congruence statement.
2x
8 cm
14 cm
A
10 cm
E
B
C
D
Chapter 6
29
Course 3
Lesson 6–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
as seen from above. The wings of the airplane form
congruent quadrilaterals, so quadrilateral ABCD quadrilateral EFGH. Use this figure for Exercises 1
and 2.
H
NAME ________________________________________ DATE ______________ PERIOD _____
6-4
Enrichment
Order of Rotational Symmetry
The two examples below show how to create designs with rotational
symmetry. In both cases, point P is the center of the rotation.
Notice that the order of rotational symmetry is the number of times the
original figure maps onto itself in a complete rotation. The first step in
making the design is to divide 360° by the order of rotation.
P
P
P
360° 8 45
Rotate 45°
and trace
Repeat 6 times.
P
Rotational Symmetry
Order 8
P
P
360° 3 120
1.
2.
4.
Order 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Rotate 120°
Repeat 1 time.
Rotational Symmetry
and trace
Write the order of rotational symmetry for each design.
3.
5.
Use a shape like the one shown to create a design with the given
center and order of rotational symmetry.
6. Order 8
7. Order 3
8. Order 5
9. Order 6
10. Order 4
11. Order 6
Chapter 6
30
Course 3