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Geometry 6.3 Big Idea: Use Similar Polygons
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Similar Polygons: Two polygons where corresponding angles are congruent and corresponding side lengths are proportional (not congruent) Symbol for similarity is ~
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Scale Factor: In two similar polygons, the ratio of the lengths of two corresponding sides. All corresponding sides have the same ratio for similar polygons.
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Theorem 6.1 Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides (scale factor).
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Example: In the diagram,
List all pairs of congruent angles. Check that the ratios of corresponding sides lengths are equal. Write ratios of the corresponding side lengths in a statement of proportionality. What is the scale factor? What is the ratio of the perimeters?
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Are these triangles similar?
If yes, what is the scale factor? What is the ratio of the perimeters?
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Example: In the diagram,
Find the value of x.
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In the diagram, Find the value of x.
What is the scale factor of QRST to ABCD?
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