7-2 Similar Polygons

Objective

To identify and apply similar polygons

Image Long Description

Similar figures have the same shape but not necessarily the same size. You can abbreviate is similar to with the symbol ∼ . tilde operator .

Essential Understanding You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures.

Take note Key Concept: Similar Polygons

Define	Diagram	Symbols
Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.	A B C D ∼ G H I J eh b c d tilde operator g h i j	∠ A ≅ ∠ G angle , eh approximately equal to , angle g ∠ B ≅ ∠ H angle , b approximately equal to , angle h ∠ C ≅ ∠ I angle , c approximately equal to , angle i ∠ D ≅ ∠ J angle , d approximately equal to , angle j A B G H = B C H I = C D I J = A D G J fraction eh b , over g h end fraction . equals . fraction b c , over h i end fraction . equals . fraction c d , over i j end fraction . equals . fraction eh d , over g j end fraction

You write a similarity statement with corresponding vertices in order, just as you write a congruence statement. When three or more ratios are equal, you can write an extended proportion. The proportion A B G H = B C H I = C D I J = A D G J fraction eh b , over g h end fraction . equals . fraction b c , over h i end fraction . equals . fraction c d , over i j end fraction . equals . fraction eh d , over g j end fraction  is an extended proportion.

A scale factor is the ratio of corresponding linear measurements of two similar figures. The ratio of the lengths of corresponding sides B C ¯ b c bar  and Y Z ¯ , y z bar , comma  or more simply stated, the ratio of corresponding sides, is B C Y Z = 20 8 = 5 2 . fraction b c , over y z end fraction . equals , 20 over 8 , equals , 5 halves , .  So the scale factor of △ A B C white up pointing triangle eh b c  to △ X Y Z white up pointing triangle x y z  is 5 2 5 halves  or 5 : 2.

△ A B C ∼ △ X Y Z white up pointing triangle eh b c tilde operator white up pointing triangle x y z

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