Similar Figures

Square Limit by M.C. Escher Escher used a pattern of squares and triangles to create Square Limit. These two triangles are similar. Similar figures have the same shape but not necessarily the same size.

Similar Figures For each part of one similar figure there is a corresponding part on the other figure. Segment AB corresponds to segment DE. B AC D E F Name another pair of corresponding segments.

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

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

AD BC 3 cm 2 cm 3 cm WZ X Y 9 cm 6 cm Corresponding sides: AB corresponds to WX. AD corresponds to WZ. CD corresponds to YZ. BC corresponds to XY.

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

Similar Figures AD BC 3 cm 2 cm 3 cm WZ X Y 9 cm 6 cm In the rectangles above, one proportion is =, or =. AB WX AD WZ 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 111 y ___ ____ = Write a proportion using corresponding side lengths. The cross products are equal = 100 y The two triangles are similar. Find the missing length y and the measure of D.

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

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

Try This 52 y ___ ____ = Write a proportion using corresponding side lengths. The two triangles are similar. Find the missing length y and the measure of B. 5,200 = 50y 5, _____ 50y 50 ___ = Divide both sides by 50 to undo the multiplication. A B 60 m120 m 50 m 100 m y 52 m 65° 45° 104 m = y

A B 60 m120 m 50 m 100 m y 52 m 65° 45° Try This The two triangles are similar. Find the missing length y and the measure of B. Angle B is congruent to angle A. If angle A = 65°, then angle B = 65°

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 w Using Proportions with Similar Figures

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

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? 36.9° 30 in. 4 in. 90° 12 ft