1. 5.2 Similar Polygons Two congruent polygons are also similar polygons.
Two polygons are similar iff (if and only if) two conditions are satisfied.
All pairs of corresponding angles are congruent.
All pairs of corresponding sides are proportional.
The symbol ~ is used to symbolize similarity.
The symbol  is used to symbolize correspondence.
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2. Similar Polygons.
The vertices of the congruent angles are corresponding vertices.
The sides opposite congruent angles are corresponding sides.
For example, in this diagram,
since A  H and B  J it follows that:
vertices A  H and A  H
B  J and B  J
and the included sides: AB  HJ
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3. Similar Triangles
If ΔABC ~ ΔDEF, find the measures of the remaining parts of each triangle.
mA =180 – = 53
Similarity of corresponding vertices tells us that:
mD = 53 mE = 90 mF = 37
The proportion that relates the length of the sides is:
AB = BC = AC
DE EF DF
3 = 4 = 5
EF DF
Solving each proportion:
EF = 8 and DF = 10 3 4
37 5 6
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