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Honors Geometry Section 8.2 B Similar Polygons

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Two polygons are congruent iff they have exactly the same size and shape. Two polygons are similar iff they have exactly the same shape.

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More formally, two polygons are similar iff their vertices can be paired so that: 1. corresponding angles are congruent 2. corresponding sides are proportional.

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For corresponding sides to be proportional, the ratios of the corresponding sides must be equal.

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To state that the polygons to the right are similar, we might write _______________ or _______________ These statements are called similarity statements.

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List 2 (of the 5) pairs of congruent angles.

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List 5 ratios that will be equal. A statement such as this is called a proportionality statement.

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Example: In the figure above, AB = 15, JF = 21, FG = 30, GH = 14, DE = 18 and EA = 10. Find all missing lengths.

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The scale factor of two similar polygons is the ratio of any pair of corresponding sides. For the figures above, the scale factor is equal to Note: You must write the scale factor in the same order as the similarity statement.

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Example: and AB = 24, BC = 32 and YZ = 40. What segment can you find the length of and what is its length? What is the scale factor for this similarity?

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