Transcript Course 3 Chapter 5 Lesson 6
7-6
Congruence
7-6
Congruence
Warm Up Find the measure of the indicated angle.
1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75° 55° 2. the third angle of a right triangle with an angle of 60° 30° 3. the supplement of a 35° angle 145°
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Congruence
Problem of the Day
The measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle? m ABC = 38°; m CBD = 52°
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Congruence
Learn
to use properties of congruent figures to solve problems.
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Congruence
Vocabulary
correspondence congruent figures
7-6
Congruence
A correspondence is a way of matching up two sets of objects. Congruent figures have the same size and shape. If two polygons are congruent, all of their corresponding sides and angle are congruent.
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Congruence
7-6
Congruence
Additional Example 1A: Writing Congruent Statements Write a congruence statement for each pair of polygons.
The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence.
A
@ Q, so A corresponds to Q.
55 55
B
@ R, so B corresponds to R.
C
@ P, so C corresponds to P.
The congruence statement is triangle ABC @ triangle QRP.
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Congruence
Additional Example 1B: Writing Congruent Statements 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
@ M, so D corresponds to M.
E
@ N, so E corresponds to N.
F
@ O, so F corresponds to O.
G
@ P, so G corresponds to P.
H
@ Q, so H corresponds to Q.
The congruence statement is pentagon
DEFGH
@ pentagon MNOPQ.
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Congruence
Check It Out: Example 1 Write a congruence statement for each pair of polygons.
The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence.
A
@ S, so A corresponds to S.
B
@ T, so B corresponds to T.
A
60° 120°
D
120°
Q
||| | |||
R
60°
C
120° 120°
B
C
@ Q, so C corresponds to Q.
D
@ R, so D corresponds to R.
T
60° | 60°
S
The congruence statement is trapezoid ABCD @ trapezoid STQR.
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Congruence
Additional Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY JKLM.
@
quadrilateral Find a.
a + 8 = 24 –8 –8 a = 16
WX
@
KL Subtract 8 from both sides.
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Congruence
Additional Example 2B: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY JKLM.
@
quadrilateral Find b.
6b = 30 6b = 30 6 6 b = 5
ML
@
YX Divide both sides by 6.
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Congruence
Additional Example 2C: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY JKLM.
Find c.
@
quadrilateral
5c = 85 5c = 85 5 5
J
@
V Divide both sides by 5.
c = 17
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Congruence
Check It Out: Example 2A In the figure, quadrilateral JIHK QRST.
@
quadrilateral Find a.
3a = 6 3a = 6 3 3 a = 2
IH
@
RS Divide both sides by 3.
H
3a 4b°
I R
6
J K
30°
Q
c + 10°
T
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Congruence
Check It Out: Example 2B In the figure, quadrilateral JIHK QRST.
Find b.
@
quadrilateral
4b = 120 4b = 120 4 4
H
@
S Divide both sides by 4.
b = 30°
H
3a 4b°
I R
6
J K
30°
Q
c + 10°
T
7-6
Congruence
Check It Out: Example 2C In the figure, quadrilateral JIHK QRST.
Find c.
@
quadrilateral
c + 10 = 30 c + 10 = 30 –10 –10
K
@
T Subtract 10 from both sides.
c = 20°
H
3a 4b°
I
90°
R
6 90°
K
30°
J Q
c + 10°
T
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Congruence
Lesson Quizzes
Lesson Quiz for Student Response Systems
7-6
Congruence
Lesson Quiz In the figure, WXYZ
@
ABCD.
1. Find XY.
10 3. Find CD.
8 2. Find m B.
80° 4. Find m Z.
90°
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Congruence
Lesson Quiz for Student Response Systems
1. In the figure, EFG @ MNO. Identify ON.
A.
11 B. 10 C. 8 D. 6
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Congruence
Lesson Quiz for Student Response Systems
2. In the figure, FGHI @ KLMN. Identify KL.
A.
3 B. 5 C. 9 D. 11
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Congruence
Lesson Quiz for Student Response Systems
3. In the figure, PQR @ XYZ. Identify m.
A.
30 B. 45 C. 60 D. 90