Similar Figures LESSON 7-4

In a proportion, the _____________________ are equal. Similar Figures LESSON 7-4 Similar Figures ____________________________________ have the same shape but not necessarily the same size. Similar Polygons If two polygons are ______________________________, then corresponding angles are congruent and the lengths of corresponding sides are in proportion.  The symbol ___________ means “is similar to.” REMEMBER: Cross Products In a proportion, the _____________________ are equal.

Is rectangle ABCD similar to rectangle RSTU? Explain why or why not. Similar Figures LESSON 7-4 Is rectangle ABCD similar to rectangle RSTU? Explain why or why not. First, check to see if corresponding angles are congruent. ∠ A ≌ ∠ R      ∠ B ≌ ∠ S ∠ C ≌ ∠ T     ∠ D ≌ ∠ U All right angles are 90°.

Next, check to see if corresponding sides are in proportion. Similar Figures LESSON 7-4 Next, check to see if corresponding sides are in proportion. AB RS DA UR AB corresponds to RS. DA corresponds to UR. 6 48 3 24 Substitute. 6 • 24 48 • 3 Write the cross products. 144 = 144 Simplify. The corresponding sides are in proportion, so rectangle ABCD is similar to rectangle RSTU.

Similar Figures LESSON 7-4 A stonemason’s sketch of a carving to be made on a building includes the letter “E” shown below. If the width of the actual letter in the arrangement is 22 in., what is the height? Set up a proportion. 2.75 in. 5 in. 22 in. x = 2.75 • x = 5 • 22 Write the cross products. Simplify. 2.75 x = 110 Divide each side by 2.75. 2.75x 2.75 110 = x = 40 Simplify. The height of the letter is 40 inches.

Similar Figures RST ~ PSU. Find the value of d. Write a proportion. 14 LESSON 7-4 RST ~ PSU. Find the value of d. Write a proportion. 14 d 12 21 = 12 • d = 21 •14 Write the cross products. Simplify. 12d = 294 Divide each side by 12. 12d 12 294 = d = 24.5 Simplify. The value of d is 24.5.