Similar Figures Susan Phillips Lee’s Summit, MO

Similar Figures For each part of one similar figure there is a corresponding part on the other figure. Corresponding: Same position, different figure B A C E Corresponding sides: AB & DE; AC & DF; BC & EF D F

Similar Figures Angle A corresponds to angle D. B Name another pair of corresponding angles. A C E D F

Similar Figures Corresponding sides have lengths that are proportional. Corresponding angles are congruent.

Similar Figures W Z X Y 9 cm 6 cm A D B C 3 cm 2 cm Corresponding sides: AB corresponds to WX. BC corresponds to XY. CD corresponds to YZ. AD corresponds to WZ.

Similar Figures W Z X Y 9 cm 6 cm A D B C 3 cm 2 cm Corresponding angles: A corresponds to W. B corresponds to X. C corresponds to Y. D corresponds to Z.

Similar Figures W Z X Y 9 cm 6 cm A D B C 3 cm 2 cm In the rectangles above, one proportion is = , or = . AB WX AD WZ 2 6 3 9 If you cannot use corresponding side lengths to write a proportion, or if corresponding angles are not congruent, then the figures are not similar.

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

The two triangles are similar. Find the missing length y. y is multiplied by 100. 22,200 100 ______ 100y 100 ____ Divide both sides by 100 to undo the multiplication. = 222 mm = y

The two triangles are similar. Find the measure of angle D. Angle D is congruent to angle C. If angle C = 70°, then angle D = 70° .

Try This 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 ___ = Write a proportion using corresponding side lengths. 5,200 = 50y 5,200 50 _____ 50y 50 ___ Divide both sides by 50 to undo the multiplication. = 104 m = y

Try This The two triangles are similar. Find the missing length y and the measure of B. A B 60 m 120 m 50 m 100 m y 52 m 65° 45° Angle B is congruent to angle A. If angle A = 65°, then angle B = 65°

Using Proportions with Similar Figures This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting? Reduced Actual 2 54 3 w

Using Proportions with Similar Figures Reduced Actual 2 54 3 w 3 cm w cm 2 cm 54 cm _____ = Write a proportion. 54 • 3 = 2 • w The cross products are equal. 162 = 2w w is multiplied by 2. Divide both sides by 2 to undo the multiplication. 81 = w

Try these 5 problems. 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