Similar and Congruent Figures

What are similar polygons?

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

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 PolygonsAngles

∠A ≅ ∠ E∠B ≅ ∠ F∠C ≅ ∠ G

ΔABC ~ ΔEFGA

B C

E

F G

Sides

AB ~ EF

AC ~ EG

BC ~ FG

Are these figures similar and/or congruent and why?

Are these figures similar and/or congruent and why?

Are these figures similar and/or congruent and why?

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.

x35 in.

15 in.

17=3

5 x = 7.3 inches

Determine the missing sides of the triangle

39 in

24 in

33 in

? in

8 in

? in

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.

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.

Similar Figures

Which of the following is not a characteristic of similar figures?A. Proportional sidesB. Equal angle measurementsC. Same shapeD. Congruent side lengths

Similar Figures

• Are the figures below similar? Explain.

Similar Figures

• Are the figures below similar? Explain.