lesson 1 menu 1.the triangles shown are similar. find x and y. 2.find the perimeter of Δdef if...
TRANSCRIPT
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.
• 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.
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.
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.
A. A
B. B
C. C
D. D
A. 3.9
B. 6
C. 7.5
D. 4.5
A. Find the geometric mean between 3 and 12.
A. A
B. B
C. C
D. D
A. 12
B. 4.9
C. 40
D. 8.9
B. Find the geometric mean between 4 and 20.
Altitude and Segments of the Hypotenuse
In ABC, BD = 6 and AD = 27. Find CD.Δ
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.
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.
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?
Draw a diagram of one of the right triangles formed.
Let be the altitude drawn from the right angle of ΔWYZ.
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.
1. A
2. B
3. C
4. D
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?
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.
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.
A. A
B. B
C. C
D. D
A. 13.9
B. 24
C. 17.9
D. 11.3
A. Find e to the nearest tenth.
A. A
B. B
C. C
D. D
A. 12.0
B. 10.3
C. 9.6
D. 8.9
B. Find f to the nearest tenth.