similar and congruent figures. what are similar polygons? two polygons are similar if corresponding...

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.

• ~

=

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.