1. GEOMETRY HELP Find the geometric mean of 3 and 12. x 2 = 36 Cross-Product Property x = 6 x = 36 Find the positive square root. The geometric mean of 3 and 12 is 6. =Write a proportion. 3x3x x 12 Quick Check Similarity in Right Triangles LESSON 7-4 Additional Examples

2. GEOMETRY HELP Solve for x and y. Use Corollary 1 of Theorem 7-3 (The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse) to find x. 2x = 36 Cross-Product Property x = 18 = Write a proportion. 2626 6x6x Similarity in Right Triangles LESSON 7-4 Additional Examples

3. GEOMETRY HELP (continued) Use Corollary 2 of Theorem 7-3 (The altitude to the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse) to find y. y 2 = 360Cross-Product Property. y = 360Find the positive square root.y = 6 10Write in the simplest radical form. = Write a proportion. xyxy y 2 + x = Substitute 18 for x. 18 y 2 + 18 Similarity in Right Triangles LESSON 7-4 Additional Examples Quick Check

4. GEOMETRY HELP At a golf course, Maria drove her ball 192 yd straight toward the cup. Her brother Gabriel drove his ball straight 240 yd, but not toward the cup. The diagram shows the results. Find x and y, their remaining distances from the cup. Use Corollary 2 of Theorem 7-3 to solve for x. 192(x +192) = 240 2 Use the Cross-Product Property. 192x + 36,864 = 57,600 Use the Distributive Property. 192x = 20,736 Solve for x. x = 108 = Write a proportion. x + 192 240 192 Similarity in Right Triangles LESSON 7-4 Additional Examples

5. GEOMETRY HELP (continued) Use Corollary 2 of Theorem 7-3 to solve for y. Maria’s ball is 108 yd from the cup, and Gabriel’s ball is 180 yd from the cup. y 2 = 32,400 Use the Cross-Product Property. y = 32,400 Find the positive square root. y = 180 = Write a proportion. x + 192 y yxyx = Substitute. 108 + 192 y 108 = Simplify. 300 y 108 Similarity in Right Triangles LESSON 7-4 Additional Examples Quick Check