Do Now 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

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 The two triangles are similar. Find the missing length y and the measure of D. 100 200 ____ 111 y ___ = 200 • 111 = 100 • y

The two triangles are similar 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°

Example 2 The two triangles are similar. Find the missing length y and the measure of B. B A 60 m 120 m 65° 50 m 100 m 45° 52 m y 50 100 ____ 52 y ___ = 100 • 52 = 50 • y

The two triangles are similar 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°

Example 3 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?

Draw a diagram to represent the situation Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. Actual Reduced 2 54 3 w

3 cm w cm 2 cm 54 cm _____ = 54 • 3 = 2 • w 162 = 2w 162 2 ____ 2w 2 ___ = 81 = w The width of the actual painting is 81 cm.

Exit Ticket 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? 30 in. 36.9° 4 in. 90° 12 ft

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

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.

Exit Ticket 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. false true No; both are quadrilaterals but they are not the same size or shape.

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