1. Lesson 1 Menu 1.The triangles shown are similar. Find x and y. 2.Find the perimeter of ΔDEF if ΔABC ~ ΔDEF, AB = 6.3, DE = 15.75, and the perimeter of ΔABC is 26.5. 3.Refer to the figure. If MN = 5, NO = 3, and NP = 7, find MQ.

2. Lesson 1 MI/Vocab geometric mean Find the geometric mean between two numbers. Solve problems involving relationships between part of a right triangle and the altitude to its hypotenuse.

3. Lesson 1 KC1

4. Lesson 1 Ex1 Geometric Mean A. Find the geometric mean between 2 and 50. Answer: The geometric mean is 10. Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify.

5. Lesson 1 Ex1 Geometric Mean B. Find the geometric mean between 25 and 7. Answer: The geometric mean is about 13.2. Definition of geometric mean Let x represent the geometric mean. Cross products Take the positive square root of each side. Simplify. Use a calculator.

6. A.A B.B C.C D.D Lesson 1 CYP1 A.3.9 B.6 C.7.5 D.4.5 A. Find the geometric mean between 3 and 12.

7. A.A B.B C.C D.D Lesson 1 CYP1 A.12 B.4.9 C.40 D.8.9 B. Find the geometric mean between 4 and 20.

8. Lesson 1 TH1

9. Lesson 1 TH2

10. Lesson 1 Ex2 Altitude and Segments of the Hypotenuse In ABC, BD = 6 and AD = 27. Find CD. Δ

11. Lesson 1 Ex2 Answer: CD is about 12.7 Altitude and Segments of the Hypotenuse Cross products Take the positive square root of each side. Use a calculator.

12. Lesson 1 CYP2 1.A 2.B 3.C 4.D A.11 B.36 C.4.7 D.8.5 Find EG. Round your answer to the nearest tenth.

13. Lesson 1 Ex3 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?

14. Lesson 1 Ex3 Draw a diagram of one of the right triangles formed. Let be the altitude drawn from the right angle of ΔWYZ.

15. Lesson 1 Ex3 Answer: The length of the long rod is 7.25 + 25.1, or about 32.4 inches long. Cross products Divide each side by 7.25.

16. 1.A 2.B 3.C 4.D Lesson 1 CYP3 A.68.3 ft B.231.3 ft C.273.1 ft D.436.1 ft AIRPLANES A jetliner has a wingspan, BD, of 211 feet. The segment drawn from the front of the plane to the tail, at point E. If AE is 163 feet, what is the length of the aircraft to the nearest tenth of a foot?

17. Lesson 1 TH3

18. Lesson 1 Ex4 Find c and d in ΔJKL. Hypotenuse and Segment of Hypotenuse

19. Lesson 1 Ex4 Hypotenuse and Segment of Hypotenuse is the altitude of right triangle JKL. Use Theorem 8.2 to write a proportion. Cross products Divide each side by 5.

20. Lesson 1 Ex4 Answer: c = 20; d ≈ 11.2 Hypotenuse and Segment of Hypotenuse is the leg of right triangle JKL. Use the Theorem 8.3 to write a proportion. Cross products Take the square root. Simplify. Use a calculator.

21. A.A B.B C.C D.D Lesson 1 CYP4 A.13.9 B.24 C.17.9 D.11.3 A. Find e to the nearest tenth.

22. A.A B.B C.C D.D Lesson 1 CYP4 A.12.0 B.10.3 C.9.6 D.8.9 B. Find f to the nearest tenth.