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Section 6.4 Similar and Congruent Figures
Objective: Identify similar and congruent figures.
similar figures ­ figures that have the same shape but not necessarily the same size
­corresponding angles of similar figures are congruent
­ratios of the lengths of corresponding sides are equal
­the symbol ~ indicates that two figures are similar Apr 9­9:27 AM
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corresponding parts ­ a pair of sides or angles that have the same relative position in two figures
Properties of Similar Figures
ABC ~ DEF
1. Corresponding angles of
similar figures are congruent
2. The ratios of the lengths of
corresponding sides of similar
figures are equal.
Apr 9­9:30 AM
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Example 1
Given LMN ~ PQR, name the corresponding angles and the corresponding sides.
M
N
L P
R
Q
Apr 9­9:40 AM
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Checkpoint pg. 289
Given ABCD ~ WXYZ, name the corresponding angles and the corresponding sides.
B
A
C
D
Y
X
Z
W
Apr 9­9:42 AM
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Example 2
Given ABCD ~ JKLM, find the ratio of the lengths of corresponding sides of ABCD to JKLM.
6 ft
M
A
8 ft
B
2 ft
4 ft
D
J
C
8 ft
12 ft
12 ft
L
3 ft
K
Apr 9­9:43 AM
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35 yd
Example 3
A soccer field is a rectangle that is 70 yards long and 40 yards wide. The penalty area of the soccer field is a rectangle that is 35 yards long and 14 yards wide. Is the penalty area similar to the field?
40 yd
14 yd
70 yd
Apr 9­9:45 AM
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Inside the penalty area of the soccer field in example 3 is a smaller rectangle known as the goal area. The goal area of soccer is 19 yards long and 6 yards wide. Is the goal similar to the penalty area? Feb 24­6:45 PM
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congruent figures ­ figures that have the same shape and the same size.
­corresponding angles and corresponding sides are congruent
­the symbol indicates that two figures are congruent
Apr 9­9:48 AM
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In the diagram, JKL PQR because:
1.
<J <P
2.
JK
<K
PQ
<L
<Q
KL QR
<R
JL
PR
J
L
Q
K
P
R
Apr 9­9:50 AM
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Example 4
Given ABCD WXYZ, find the indicated measure.
a. WZ
B
A
105 12 m
D
80
C
b. m<W
Y
X
16 m
W
Z
Apr 9­9:51 AM
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The outline of the frame of a house is a rectangle that is 45 feet long and 24 feet high. The garage is attached to the house and
the outline of its frame is 30 feet long and 16 feet high. Is the garage similar to the house? Apr 9­10:30 AM
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