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

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SIMILAR AND CONGRUENT

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

Page 1: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILA

R AND C

ONGRUENT

Page 2: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

CONGRUENT FIGURES

In order to be congruent, two figures must be the same size and same shape.

~ =

Page 3: 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.

Page 4: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILAR FIGURES

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

Page 5: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

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

Page 6: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

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.

Page 7: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILAR? CONGRUENT? NEITHER?

Page 8: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILAR? CONGRUENT? NEITHER?

5 5

Page 9: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILAR? CONGRUENT? NEITHER?

7 42

5 40

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SIMILAR? CONGRUENT? NEITHER?

72

9

14

112

Page 11: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

PROPORTIONS

Page 12: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

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

Page 13: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SOLVE FOR X.

x 30

12 in.x in.

40 in. 30 in..

40=12 x = 9 inches

Page 14: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SOLVE FOR X. ROUND TO THE NEAREST TENTH.

4 x

12 in.

4 in.

20 in.

x in..

20=12 x = 6.7 inches

Page 15: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SOLVE FOR X.

7 25

14 m.7 m.

x 25 m.

x=14 x = 50 meters

Page 16: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SOLVE FOR X. ROUND TO THE NEAREST TENTH.

15 x

17 in.

x

35 in.

15 in.

17=35 x = 7.3 inches

Page 17: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

DETERMINE THE MISSING SIDES OF THE TRIANGLE

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39 in

24 in

33 in

? in

8 in

? in

Page 18: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

SIMILA

R FIG

URES

PRACTI

CE

Page 19: SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size and same shape. ~ =

12

3

28X

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15

6

24

y

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14

2

1b

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48 6

9t

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126 14

12G

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84

12

8

D