Transcript Fractions and Decimals - Sweet Home School District

Similar & Congruent Figures
Recognize congruent and similar figures.
Find the scale factor of similar figures.
2each16proportion.
Solve
15

c
1.
1 .5 a
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3 12
2.
3.
Casey spent $31.50 for 9 tickets to the school carnival.
How much would 3 tickets to the school carnival cost?
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Similar:
◦ same shape, different size.
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Corresponding Parts:
◦ The angles and sides in similar or congruent figures that match.
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Congruent:
◦ Equal in measure (identical twins)
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Scale Factor:
◦ The ratio of corresponding sides in two similar figures.
1.
Corresponding angles are congruent.
2.
The measures of corresponding sides are
proportional.
ΔDOT is similar to ΔSUN.
Find the scale factor
from ΔDOT to ΔSUN.
6
10
6 3

10 5
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Write a ratio of corresponding sides.
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Simplify the ratio.
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3
The scale factor from ΔDOT to ΔSUN is
or 3 : 5.
5
Determine whether rectangle CARS is similar to rectangle
BIKE. If so, find the scale factor.
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All corresponding angles are congruent.
CA 2
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BI 3
SC 4 2
 
EB 6 3
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Find the ratio of corresponding heights.
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Find the ratio of corresponding lengths.
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The corresponding angles are congruent and the
corresponding sides have equal ratios so CARS ~ BIKE.
The scale factor is 2 or 2 : 3.
3
Consider the two squares above. Are the two squares
similar? Explain.
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Each angle is 90⁰, all corresponding angles are equal.
The ratio of any two corresponding sides is:
5 1
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5 1
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Yes, the squares are similar. They have a scale factor
of 1 : 1.
Is Rectangle A similar
to Rectangle B?
 All corresponding angles are equal (90⁰).
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Find ratio of long sides.
Find ratio of short sides.
6
7
3
4
Ratios not equal so sides
are not proportional.
Rectangle A is NOT similar to Rectangle B.
Is Rectangle A similar to
Rectangle C?
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All corresponding angles are equal (90⁰).
6 1
Find ratio of long sides. 12  2
Ratios are equal so sides
are proportional.
3 1
Find ratio of short sides: 6  2
Yes Rectangle A is similar to Rectangle C.
1.
Find the corresponding sides and corresponding angles to
the ones given for the pair of similar figures.
P
A
U
4
3
K
S
6
R
PA corresponds to ______
AR corresponds to _____
RK corresponds to _____
KP corresponds to _____
Y
N
8
P  _____
A  _____
R  _____
K  _____
Determine the scale factor for each pair of similar
figures.
2)
15
3)
35
45
15
16
48
What is an example of two congruent figures in your
home? What is an example of two similar figures in your
home?