Transcript Course 3 Chapter 5 Lesson 6
8-6 Congruent Polygons Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
8-6 Congruent Polygons 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°
Holt CA Course 1
8-6 Congruent Polygons California Standards
MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures.
Holt CA Course 1
8-6 Congruent Polygons
Vocabulary
correspondence congruent
Holt CA Course 1
8-6 Congruent Polygons
A correspondence is a way of matching up two sets of objects. Congruent figures have the same shape and size. If two polygons are congruent, all of their corresponding sides and angles are congruent. To write a congruence statement, the vertices in the second polygon have to be written in order of correspondence with the first polygon.
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 1: Writing Congruent Statements A. Write a congruence statement for each pair of polygons.
A corresponds to Q.
B corresponds to R.
C corresponds to P.
A
@
Q
B
@
R
C
@
P
55 55 The congruence statement is triangle ABC @ triangle QRP.
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 1: Writing Congruent Statements B. 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 corresponds to M.
D
@
M
E corresponds to N.
E
@
N
F corresponds to O.
F
@
O
G corresponds to P.
G
@
P
H corresponds to Q.
H
@
Q
The congruence statement is pentagon
DEFGH
@ pentagon MNOPQ.
Holt CA Course 1
8-6 Congruent Polygons
Check It Out!
Example 1 A. Write a congruence statement for each pair of polygons.
A corresponds to S.
A
@
S A
60° | 60°
B
B corresponds to T.
B
@
T
C corresponds to Q.
D corresponds to R.
C
@
Q
D
@
R
120°
D
120°
Q
||| |||
C
120°
R
120° The congruence statement is trapezoid ABCD @ trapezoid STQR.
T
60° | 60°
S
Holt CA Course 1
8-6 Congruent Polygons
Check It Out!
Example 1 B. Write a congruence statement for each pair of polygons.
A corresponds to M.
B corresponds to N.
C corresponds to O.
D corresponds to P.
E corresponds to Q.
F corresponds to L.
A
@
M
B
@
N
C
@
O
D
@
P
E
@
Q
F
@
L
The congruence statement is hexagon
ABCDEF
@ hexagon MNOPQL.
A
110° 110°
B F
140° 140° 110°
E
110°
D
110°
N M
110° 140°
O C L
140° 110°
Q
110°
P
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 2: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY
@
quadrilateral JKLM.
A. Find a.
a + 8 = 24 –8 –8 a = 16
WX
@
KL Subtract 8 from both sides.
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 2: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY JKLM.
@
quadrilateral B. Find b.
6b = 30 6b = 30 6 6 b = 5
ML
@
YX Divide both sides by 6.
Holt CA Course 1
8-6 Congruent Polygons
Additional Example 2: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY JKLM.
C. Find c.
@
quadrilateral
5c = 85 5c = 85 5 5
J
@
V Divide both sides by 5.
c = 17
Holt CA Course 1
8-6 Congruent Polygons
Check It Out!
Example 2 In the figure, quadrilateral JIHK QRST.
@
quadrilateral A. 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
Holt CA Course 1
8-6 Congruent Polygons
Check It Out!
Example 2 In the figure, quadrilateral JIHK QRST.
B. 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
Holt CA Course 1
8-6 Congruent Polygons
Check It Out!
Example 2 In the figure, quadrilateral JIHK QRST.
C. 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
Holt CA Course 1
8-6 Congruent Polygons
Lesson Quiz
1. The figures above are congruent. Write a congruence statement.
WXYZ
@
ABCD
2. Find XY.
10 3. Find m B.
80° 4. Find CD.
8 3. Find m Z.
90°
Holt CA Course 1