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

SIMILA

R AND C

ONGRUENT

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

ΔABC ~ ΔEFGA

B C

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?

SIMILAR? CONGRUENT? NEITHER?

5 5

SIMILAR? CONGRUENT? NEITHER?

7 42

5 40

SIMILAR? CONGRUENT? NEITHER?

72

9

14

112

PROPORTIONS

YOU CAN FIND THE MISSING LENGTH OF A SIDE IN A PAIR OF SIMILAR FIGURES, BY USING PROPORTIONS

6 7

ΔRST ~ ΔUVW

R

ST

U

V W

x ft.

6 ft.

35 ft. 7 ft.

35=x x = 30 feet

SOLVE FOR X.

x 30

12 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.

7 25

14 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

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39 in

24 in

33 in

? in

8 in

? in

SIMILA

R FIG

URES

PRACTI

CE

12

3

28X

15

6

24

y

14

2

1b

48 6

9t

126 14

12G

84

12

8

D