Course 3 Chapter 5 Lesson 6

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7-6
Congruence
M8G1.d Understand the meaning of congruence.
Warm Up
Problem of the Day
Lesson Presentation
CW/HW Assignments
Course 3
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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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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
4
Learn to use properties of congruent figures to
solve problems.
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Vocabulary
correspondence
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A correspondence is a way of matching up two sets
of objects.
If two polygons are congruent, all of their
corresponding sides and angles are congruent. In
a congruence statement, the vertices in the
second polygon are written in order of
correspondence with the first polygon.
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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 _at_ ?Q, so ?A corresponds to ?Q.
?B _at_ ?R, so ?B corresponds to ?R.
?C _at_ ?P, so ?C corresponds to ?P.
The congruence statement is triangle ABC _at_
triangle QRP.
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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 _at_ ?M, so ?D corresponds to ?M.
?E _at_ ?N, so ?E corresponds to ?N.
?F _at_ ?O, so ?F corresponds to ?O.
?G _at_ ?P, so ?G corresponds to ?P.
?H _at_ ?Q, so ?H corresponds to ?Q.
The congruence statement is pentagon DEFGH _at_
pentagon MNOPQ.
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Check It Out Example 1A
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
B

60
60


120
120

D
C
?A _at_ ?S, so ?A corresponds to ?S.
Q
R

120
120
?B _at_ ?T, so ?B corresponds to ?T.


?C _at_ ?Q, so ?C corresponds to ?Q.
60
60

?D _at_ ?R, so ?D corresponds to ?R.
S
T
The congruence statement is trapezoid ABCD _at_
trapezoid STQR.
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Check It Out Example 1B
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.
110
A
B
?A _at_ ?M, so ?A corresponds to ?M.
110
140
140
?B _at_ ?N, so ?B corresponds to ?N.
F
C
110
?C _at_ ?O, so ?C corresponds to ?O.
D
E
110
N
?D _at_ ?P, so ?D corresponds to ?P.
110
O
M
?E _at_ ?Q, so ?E corresponds to ?Q.
140
110
110
P
?F _at_ ?L, so ?F corresponds to ?L.
140
L
The congruence statement is hexagon ABCDEF _at_
hexagon MNOPQL.
110
Q
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Additional Example 2A Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY _at_ quadrilateral
JKLM.
Find a.
Subtract 8 from both sides.
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Additional Example 2B Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY _at_ quadrilateral
JKLM.
Find b.
Divide both sides by 6.
b 5
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Additional Example 2C Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY _at_ quadrilateral
JKLM.
Find c.
Divide both sides by 5.
c 17
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Check It Out Example 2A
In the figure, quadrilateral JIHK _at_ quadrilateral
QRST.
Find a.
Divide both sides by 3.
3a
I
H
a 2
6
4b
S
R
120
J
30
Q
K
c 10
T
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Check It Out Example 2B
In the figure, quadrilateral JIHK _at_ quadrilateral
QRST.
Find b.
Divide both sides by 4.
3a
I
H
b 30
6
4b
S
R
120
J
30
Q
K
c 10
T
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Check It Out Example 2C
In the figure, quadrilateral JIHK _at_ quadrilateral
QRST.
Find c.
Subtract 10 from both sides.
3a
I
H
c 20
6
90
4b
S
R
120
90
J
30
Q
c 10
K
T
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Lesson Quiz
In the figure, WXYZ _at_ ABCD
2. Find m?B.
10
80
8
90
4. Find m?Z.
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Assignmenst

• Class Work Guided and Independent Practice
  problems 1-8 (all), page 356.
• Homework Problems 12-28 (even), pages 356-
  357.