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SIMILAR AND CONGRUENT

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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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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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SIMILAR FIGURES Similar figures must be the same shape, but their sizes may be different. They have to be what we call proportional.

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ANGLES AND SIDES IN SIMILAR POLYGONS Angles ∠A ≅ ∠ E ∠B ≅ ∠ F ∠C ≅ ∠ G Δ ABC ~ Δ EFG A BC E F G Sides AB ~ EF AC ~ EG BC ~ FG

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PROPORTIONAL? In order for a figure to be considered proportional the figures have their sides have to create the same reduced fraction. 12 in. 20 in. 4 in. 5 in.

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SIMILAR? CONGRUENT? NEITHER?

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5 5

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7 42 5 40

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SIMILAR? CONGRUENT? NEITHER? 72 9 14 112

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PROPORTIONS

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YOU CAN FIND THE MISSING LENGTH OF A SIDE IN A PAIR OF SIMILAR FIGURES, BY USING PROPORTIONS 6 7 ΔRST ~ ΔUVW R S T U V W x ft. 6 ft. 35 ft. 7 ft. 35 = x x = 30 feet

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SOLVE FOR X. x 30 12 in. x in. 40 in. 30 in.. 40 = 12 x = 9 inches

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SOLVE FOR X. ROUND TO THE NEAREST TENTH. 4 x 12 in. 4 in. 20 in. x in.. 20 = 12 x = 6.7 inches

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SOLVE FOR X. 7 25 14 m. 7 m. x 25 m. x = 14 x = 50 meters

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SOLVE FOR X. ROUND TO THE NEAREST TENTH. 15 x 17 in. x 35 in. 15 in. 17 = 35 x = 7.3 inches

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DETERMINE THE MISSING SIDES OF THE TRIANGLE 39 in 24 in 33 in ? in 8 in ? in

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SIMILAR FIGURES PRACTICE

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12 3 28 X

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15 6 24 y

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14 2 1b

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48 6 9 t

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126 14 12 G

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84 12 8 D

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