Learn to use proportions to find missing measures in similar figures.

1. Learn to use proportions to find missing measures in similar figures.

2. Vocabulary corresponding sides corresponding angles similar

3. Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

4. Similar figures have the same shape but not necessarily the same size.

5. The two triangles are similar. Find the missing length y and the measure of D. 111 100 ___ ____ y 200 Additional Example 1: Finding Missing Measures in Similar Figures Write a proportion using corresponding side lengths. = 200 • 111= 100 •y The cross products are equal.

6. The two triangles are similar. Find the missing length y and the measure of D. 100 111 ____ 200 y Additional Example 1 Continued 22,200 22,200 Cross multiply…both sides equal 22,200. . ____ = 22,200 ÷ 100 = 222 mm Divide by 100. Angle D is congruent to angle C, and m C = 70°. m D = 70°

7. 52 50 ___ ____ y 100 Check It Out: Example 1 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 52 m 45° y Write a proportion using corresponding side lengths. = 100 • 52= 50 •y The cross products are equal.

8. 50 52 ___ _____ 100 y Check It Out: Example 1 Continued The two triangles are similar. Find the missing length y and the measure of B. 5,200 5,200 Cross multiply...both sides equal 5200. = 5200 ÷ 50 = 104 m y Divide by 50. Angle B is congruent to angle A, and m A = 65°. m B = 65°

9. Lesson Quiz 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