Transcript Course 3 Chapter 5 Lesson 6

5-6
5-6 Congruence
Congruence
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
5-6
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
Pre-Algebra
145°
5-6
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°
Pre-Algebra
5-6
Congruence
Learn to use properties of congruent
figures to solve problems.
Pre-Algebra
5-6
Congruence
Vocabulary
correspondence
Pre-Algebra
5-6
Congruence
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.
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
Additional Example 1B: 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.
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
T
|||
Q
|||
60°
|
120°
C @ Q, so C corresponds to Q.
D @ R, so D corresponds to R.
60°
120°
A @ S, so A corresponds to S.
|
60°
B
120°
C
R 120°
60°
S
The congruence statement is trapezoid ABCD @ trapezoid STQR.
Pre-Algebra
5-6
Congruence
Try This: Example 1B
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
B
A @ M, so A corresponds to M.
110°
B @ N, so B corresponds to N.
C @ O, so C corresponds to O.
F 140° 140° C
110°E
110°N
D @ P, so D corresponds to P.
E @ Q, so E corresponds to Q.
F @ L, so F corresponds to L.
The congruence statement is hexagon
ABCDEF @ hexagon MNOPQL.
Pre-Algebra
110°
D
M 110° 140° O
L
140° 110° P
Q 110°
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.
H 3a I
4b° 90°
c = 20°
K
30°
J
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.
80°
3. Find CD.
8
4. Find mZ.
90°
Pre-Algebra