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Similar Polygons

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**What are similar polygons?**

Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.

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Congruent Figures In order to be congruent, two figures must be the same size and same shape. ~ =

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Similar Figures Similar figures must be the same shape, but their sizes may be different. ~

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**Angles and Sides in Similar Polygons**

∠A ≅ ∠ E ∠B ≅ ∠ F ∠C ≅ ∠ G Sides AB ~ EF AC ~ EG BC ~ FG A ΔABC ~ ΔEFG E B C F G

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**You can find the missing length of a side in a pair of similar figures, by using proportions**

ΔRST ~ ΔUVW R x ft. U 6 ft. S T W V 35 ft. 7 ft. x = 30 feet = x 35

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Solve for x. 40 in. 30 in.. 12 in. x in. x x = 9 inches = 12 40

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**Solve for x. Round to the nearest tenth.**

12 in. 4 in. 20 in. x in.. x x = 6.7 inches = 12 20

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Solve for x. x 25 m. 14 m. 7 m. x = 50 meters = 14 x

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**Solve for x. Round to the nearest tenth.**

17 in. x 35 in. 15 in. x x = 7.3 inches = 35 17

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**Determine the missing sides of the triangle**

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**Determine the length of the missing side**

Two rectangles are similar. The first is 4 in. wide and 15 in. long. The second is 9 in. wide. Find the length of the second rectangle.

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**Determine the length of the missing side**

Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.

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Similar Figures Which of the following is not a characteristic of similar figures? A. Proportional sides B. Equal angle measurements C. Same shape D. Congruent side lengths

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Similar Figures Are the figures below similar? Explain.

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Similar Figures Are the figures below similar? Explain.

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