Congruence
5-6
Pre-Algebra
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°
Learn to use properties of congruent figures
to solve problems.
Vocabulary
correspondence
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.
Example: 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.
Example: Writing Congruent Statements
Write a congruence statement for the 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.
Try This
Write a congruence statement for the pair of
polygons.
The first trapezoid can be named A B
|
trapezoid ABCD. To complete the 60° 60°
congruence statement, the vertices in
the second trapezoid have to be written
120° 120°
in order of the correspondence. D
|||
C
A @ S, so A corresponds to S.
Q ||| R 120°
120°
B @ T, so B corresponds to T.
C @ Q, so C corresponds to Q.
60° | 60°
D @ R, so D corresponds to R. T S
The congruence statement is trapezoid ABCD @ trapezoid STQR.
Try This
Write a congruence statement for the pair of
polygons.
The vertices in the first pentagon are written in order
around the pentagon starting at any vertex. 110°
A @ M, so A corresponds to M. A B
110°
B @ N, so B corresponds to N. F 140° 140° C
110°
C @ O, so C corresponds to O.
E
110° D
D @ P, so D corresponds to P. 110°N
E @ Q, so E corresponds to Q. M 110° 140° O
F @ L, so F corresponds to L. 140° 110° P
The congruence statement is hexagon
L
ABCDEF @ hexagon MNOPQL. Q 110°
Example: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
A. Find a.
a + 8 = 24 WX @ KL
–8 –8 Subtract 8 from both sides.
a = 16
Example: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
B. Find b.
6b = 30 ML @ YX
6b = 30 Divide both sides by 6.
6 6
b=5
Example: Using Congruence
Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral
JKLM.
C. Find c.
5c = 85 J @ V
5c = 85 Divide both sides by 5.
5 5
c = 17
Try This
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
A. Find a.
3a = 6 IH @ RS
3a = 6
Divide both sides by 3.
3 3
a= 2 H 3a I
4b° R 6 S
120°
30° J
K Q c + 10°
T
Try This
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
B. Find b.
4b = 120 H @ S
4b = 120 Divide both sides by 4.
4 4
H 3a I
b = 30° 4b° R 6 S
120°
30° J
K Q c + 10°
T
Try This
In the figure, quadrilateral JIHK @ quadrilateral
QRST.
C. Find c.
c + 10 = 30 K @ T
c + 10 = 30 Subtract 10 from both sides.
–10 –10
c = 20° H 3a I
4b° 90° R 6 S
90°120°
30° J
K Q c + 10°
T
Lesson Quiz
In the figure, WXYZ @ ABCD
1. Find XY. 10 2. Find mB. 80°
3. Find CD. 8 4. Find mZ. 90°