True or false?

1. Some trapezoids are parallelograms.

2. Some figures with 4 right angles are squares.

3. Some quadrilaterals have only one right angle.

false

true

true

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3/18/2015 8-3 D Similar & Congruent Figures

• Similar figures- have the same shape but not necessarily the same size– The measures of the corresponding angles are

equal– The ratios of the lengths of the corresponding

sides are proportional

corresponding sides- matching sides of two or more polygons

corresponding angles- matching angles

Example 1

111 y

___ 100 200

____ =

200 • 111 = 100 • y

The two triangles are similar. Find the missing length y and the measure of D.

22,200 = 100y

22,200 100

______ 100y 100

____ =

222 mm = y

Angle D is congruent to angle C, and m C = 70°.

m D = 70°

The two triangles are similar. Find the missing length y and the measure of D.

Example 2

52 y

___ 50 100

____ =

100 • 52 = 50 • y

A B60 m 120 m

50 m 100 m

y52 m

65°

45°

The two triangles are similar. Find the missing length y and the measure of B.

5,200 = 50y

5,200 50

_____ 50y 50

___ =

104 m = y

Angle B is congruent to angle A, and m A = 65°.

m B = 65°

The two triangles are similar. Find the missing length y and the measure of B.

This reduction is similar to a picture that Nicole painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting?

Example 3

Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.

ReducedActual

2 54

3w

54 • 3 = 2 • w

162 = 2w

162 2

____ 2w 2

___ =

81 = w

The width of the actual painting is 81 cm.

3 cm w cm

2 cm 54 cm

_____ =

These two triangles are similar.

1. Find the missing length x.

2. Find the measure of J.

3. Find the missing length y.

4. Find the measure of P.

5. Susan is making a wood deck from plans for an

8 ft by 10 ft deck. However, she is going to

increase its size proportionally. If the length is

to be 15 ft, what will the width be?

36.9°

30 in.

4 in.

90°

12 ft

Exit Ticket

1. These two triangles are similar. Identify

the missing length x.

A. 3 cm B. 4 cm C. 5 cm D. 6 cm

2. These two triangles are similar. Identify

the measure R.

A. 30 B. 50 C. 80 D. 90

3. These two triangles are similar. Identify

the missing length y.

A. 27 in. B. 21 in. C. 9 in. D. 8 in.

4. A carpenter is making a rectangular table

top of dimensions 9 ft by 12 ft. However, he is

going to increase its size proportionally. If

the width is to be 15 ft, what will the length

be?

A. 24 ft B. 20 ft C. 18 ft D. 12 ft

congruent figures- have the same shape and same size

-the corresponding sides and corresponding angles are congruent.

Example 1

These figures are NOT congruent.

Decide whether the figures in each pair are congruent. If not, explain.

Example 2

These figures are congruent.

Example 3

These figures are congruent.

Example 4

These figures are congruent.

Example 5

Jodi needs a sleeping pad that is congruent to her sleeping bag. Which pad should she buy?

Sleeping pad B is congruent to the sleeping bag.

True or false?

1. If two figures have sides of the same length, they are congruent.

2. Congruent figures have angle measures that are equal.

3. Decide whether the figures are congruent. If not, explain.

true

false

No; both are quadrilaterals but they are not the same size or shape.

Exit Ticket

Homework

• Pg. 483 #1-32 Evens• Study quiz tomorrow!!!