SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

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Presentation transcript:

SIMILAR AND CONGRUENT

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

WHAT ARE SIMILAR POLYGONS? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.

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

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

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.

SIMILAR? CONGRUENT? NEITHER?

5 5

SIMILAR? CONGRUENT? NEITHER?

PROPORTIONS

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

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

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

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

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

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

SIMILAR FIGURES PRACTICE

X

y

14 2 1b

t

G

D

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