Transcript Course 3 Chapter 5 Lesson 6

5-6
Congruence
Learn to use properties of congruent
figures to solve problems.
Pre-Algebra
5-6
Congruence
If two polygons are congruent, all of their
corresponding sides and angles are
congruent.
A corresponding sides are the sides of
two congruent shapes that are in the
same spot on each shape and are the
same measure.
Pre-Algebra
5-6
Congruence
Additional Example 1A: Writing Congruent Statements
Write a congruence statement for the 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.
B @ R, so B corresponds to R.
C @ P, so C corresponds to P.
The congruence statement is triangle ABC @ triangle QRP.
Pre-Algebra
5-6
Congruence
Try This: Example 1A
Write a congruence statement for the 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 @ T, so B corresponds to T.
D
Q
120°
C @ Q, so C corresponds to Q.
D @ R, so D corresponds to R.
60°
120°
A @ S, so A corresponds to S.
T
|
60°
|||
|||
|
60°
B
120°
C
R 120°
60°
S
The congruence statement is trapezoid ABCD @ trapezoid STQR.
Pre-Algebra
5-6
Congruence
Additional Example 2A: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
A. Find a.
a + 8 = 24
–8
–8
a = 16
Pre-Algebra
WX @ KL
Subtract 8 from both sides.
5-6
Congruence
Additional Example 2B: 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
Pre-Algebra
ML @ YX
Divide both sides by 6.
5-6
Congruence
Additional Example 2C: 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
Pre-Algebra
5-6
Congruence
Try This: Example 2A
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
Pre-Algebra
30°
J
Q
S
120°
c + 10°
T
5-6
Congruence
Try This: Example 2B
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
Pre-Algebra
30°
J
R 6
S
120°
Q
c + 10°
T
5-6
Congruence
Try This: Example 2C
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.
c = 20°
K
H 3a I
4b 90
° °
J
30°
R 6 S
90 120°
°
Q c + 10°
T
Pre-Algebra
5-6
Congruence
Lesson Quiz
In the figure, WXYZ @ ABCD
1. Find XY.
10
2. Find mB.
3. Find CD.
8
4. Find mZ.
Pre-Algebra
80
°
90°