8-6 Congruent Polygons
California
Standards
MG3.4 Demonstrate an understanding
of conditions that indicate two geometrical
figures are congruent and what congruence
means about the relationship between the sides
and angles of the two figures.
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8-6 Congruent Polygons
A correspondence is a way of matching up two
sets of objects.
Congruent figures have the same shape and
size. If two polygons are congruent, all of their
corresponding sides and angles are congruent.
To write a congruence statement, the vertices in
the second polygon have to be written in order of
correspondence with the first polygon.
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8-6 Congruent Polygons
Additional Example 1: Writing Congruent Statements
A. Write a congruence statement for each pair of
polygons.
A corresponds to Q.
A @ Q
B corresponds to R.
B @ R
55
55
C corresponds to P.
C @ P
The congruence statement is triangle ABC @ triangle QRP.
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 1: Writing Congruent Statements
B. Write a congruence statement for each pair of
polygons.
The vertices in the first pentagon are written in order
around the pentagon starting at any vertex.
D corresponds to M. D @ M
E corresponds to N. E @ N
F corresponds to O. F @ O
G corresponds to P. G @ P
H corresponds to Q. H @ Q
The congruence statement is pentagon
DEFGH @ pentagon MNOPQ.
Holt CA Course 1
8-6 Congruent Polygons
Check It Out! Example 1
A. Write a congruence statement for each pair of
polygons.
A corresponds to S.
A @ S
B corresponds to T.
B @ T
C corresponds to Q.
C @ Q
D corresponds to R.
D @ R
The congruence statement is
trapezoid ABCD @ trapezoid STQR.
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A
60°
120°
D
|||
Q
|||
60°
|
120°
T
|
60°
B
120°
C
R 120°
60°
S
8-6 Congruent Polygons
Check It Out! Example 1
B. Write a congruence statement for each pair of
polygons.
A corresponds to M.
A @ M
B corresponds to N.
B @ N
C corresponds to O.
C @ O
D corresponds to P.
D @ P
E corresponds to Q.
E @ Q
F corresponds to L.
F @ L
The congruence statement is hexagon
ABCDEF @ hexagon MNOPQL.
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A
110°
110°
B
F 140° 140° C
110°E
110°
110°N
D
M 110° 140° O
L
140° 110° P
Q 110°
8-6 Congruent Polygons
Additional Example 2: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
A. Find a.
a + 8 = 24
–8
–8
a = 16
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WX @ KL
Subtract 8 from both sides.
8-6 Congruent Polygons
Additional Example 2: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
B. Find b.
6b = 30
6b = 30
6
6
b=5
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ML @ YX
Divide both sides by 6.
8-6 Congruent Polygons
Additional Example 2: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
C. Find c.
5c = 85
J @ V
5c = 85
5
5
Divide both sides by 5.
c = 17
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8-6 Congruent Polygons
Check It Out! Example 2
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
A. Find a.
3a = 6
3a = 6
3
3
a= 2
IH @ RS
Divide both sides by 3.
H 3a I
4b°
R 6
K
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30°
J
Q
S
120°
c + 10°
T
8-6 Congruent Polygons
Check It Out! Example 2
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
B. Find b.
4b = 120
H @ S
4b = 120
4
4
Divide both sides by 4.
H 3a I
4b°
b = 30
K
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30°
J
R 6
S
120°
Q
c + 10°
T
8-6 Congruent Polygons
Check It Out! Example 2
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
C. Find c.
c + 10 = 30
K @ T
c + 10 = 30
–10 –10
Subtract 10 from both sides.
H 3a I
4b° 90°
c = 20
K
30°
J
R 6 S
90°120°
Q
c + 10°
T
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