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Similar Polygons. Circle Limit III M.C. Escher. Figures that are similar (~) have the same shape but not necessarily the same size. Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing - PowerPoint PPT Presentation
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Circle Limit IIIM.C. Escher
Figures that are similar (~) have the same shape but not necessarily the same size.
Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.
Two polygons are similar polygons if and only if their corresponding angles are congruent & their corresponding side lengths are proportional.
All the angles are the same
All sides areproportional
Similar Polygons – 2 polygons that have the same shape but not the same size.
Symbol ( ~ ) Corresponding s are . Corresponding sides are Proportional.
Equal Ratios:
** Reduce to the same fraction!!
Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math
Ex: Order Matters ΔABC ~ ΔXYZ
A
B
C
10
X
Y
Z42
78
BC corresponds to YZ
mB =
mC =
78
60
Find AB:
4 6
8
410
= 6AB AB = 15
410
= 8AC AC = 20Find AC:
Example : Identifying Similar Polygons
Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
rectangles ABCD and EFGH
Example 3
A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.
Example 3 Continued
1.25(36.25) = x(9) Cross Products Prop.45.3 = 9x Simplify.
5 x Divide both sides by 9.
The length of the model is approximately 5 inches.
Ex. 2: Are the following polygons similar?
1in
B C
DA
K L
MJ
2in
2in
4in 4in
1in
2in
1in
2in
1) Check to see if all s are ?
2) Check the ratio of all corresponding sides?
120
80