1. Lesson 7-1 Geometric Means Theorem 7.1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and each other Theorem 7.2 The measure of an altitude drawn from a vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the two segments of the hypotenuse

2. Theorems (con’t) Theorem 7.3 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the measure of the leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

3. Find the geometric mean between 2 and 50. Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify. Answer: The geometric mean is 10.

4. Find the geometric mean between 25 and 7. Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify. Answer: The geometric mean is about 13.2. Use a calculator.

5. a. Find the geometric mean between 3 and 12. b. Find the geometric mean between 4 and 20. Answer: 6 Answer: 8.9

7. Cross products Take the positive square root of each side. Use a calculator. Answer: CD is about 12.7.

8. Answer: about 8.5

9. KITES Ms. Alspach is constructing a kite for her son. She has to arrange perpendicularly two support rods, the shorter of which is 27 inches long. If she has to place the short rod 7.25 inches from one end of the long rod in order to form two right triangles with the kite fabric, what is the length of the long rod?

10. Draw a diagram of one of the right triangles formed. Let be the altitude drawn from the right angle of

11. Cross products Divide each side by 7.25. Answer: The length of the long rod is 7.25 + 25.2, or about 32.4 inches long.

12. AIRPLANES A jetliner has a wingspan, BD, of 211 feet. The segment drawn from the front of the plane to the tail, intersects at point E. If AE is 163 feet, what is the length of the aircraft? Answer: about 231.3 ft

13. Find c and d in

14. is the altitude of right triangle JKL. Use Theorem 7.2 to write a proportion. Cross products Divide each side by 5.

15. is the leg of right triangle JKL. Use the Theorem 7.3 to write a proportion. Answer: Cross products Take the square root. Simplify. Use a calculator.

16. Find e and f. Answer: f