Chapter 9 Test Review with Key

Geometry B 

Chapter 9 Test Review Name_______________________ 

1. Solve for a and b. 

10 

6 

8 

2. Find a, b, and h. 

a 

h 

b 

b 

5 15 

a 

3. Find the length of the altitude drawn to the hypotenuse. 

4 19 

[1] 

[2] 

[3]

Geometry B 


4. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places. 

27 

22 

a 

5. Find the area of this right triangle if b = 7 and c = 74 . 

c 

b 

6. Choose the sets that are possible sides of a right triangle. 

A. 4, 9, 13 

B. 2 , 2 , 2 

C. 8, 15, 17 

D. 1, 1, 2 

a 

[4] 

[5] 

[6]

Geometry B 


7. For each set of numbers, determine whether the numbers represent the lengths of the sides 

of an acute triangle, a right triangle, an obtuse triangle, or no triangle. 

A. 32, 25, 9 

B. 16, 30, 34 

C. 1.8, 9.6, 20.1 

8. Find the value of x and y . 

x 

18 

45° 30° 

y 

9. Find the value of x and y . 

y 

30° 

x 

21 

[7] 

[8] 

[9] 

10. You are creating quilting blocks out of squares. If a block has a side of length 3 centimeters, 

how long is each diagonal to the nearest tenth of a centimeter? 

[10]

Geometry B 


11. Write sin A. 

13 

A 12 

C 

12. Find sin P, cos P, tan P. 

5 

B 

5 

12 

13 

[11] 

P 

[12] 

13. A slide 4.8 m long makes an angle of 28° with the ground. How high is the top of the slide 

above the ground? 

[13] 

14. Find the value of x, to the nearest whole number. (not drawn to scale) 

A 

x 

C 

5 

37° 

B 

[14]

Geometry B 


15. Find x, to the nearest hundredth. 

14 

x 

32° 

16. An antenna is atop the roof of a 100-foot building, 10 feet from the edge, as shown in the 

figure below. From a point 50 feet from the base of the building, the angle from ground 

level to the top of the antenna is 66°. Find x, the length of the antenna, to the nearest foot. 

66° 

50 ft 

17. Given J 3, – 1 

x 

10 ft 

b g and K 2 5 

[15] 

[16] 

b , g, find the magnitude of JK v to the nearest tenth. 

[17] 

18. If v b = 〈 – 1,– 7 〉 and v c = 〈 – 1, 4 〉 , what is v b + v c ? 

[18]

Geometry B 


19. Find the sum of the pair of vectors. Express your answer in ordered pair form. 

y 

10 

–10 10 x 

–10 

[19] 

20. Prove the Pythagorean Theorem using an informal two-column proof. The labeled diagram 

shows the altitude drawn from C to D, 

creating similar right triangles. Use geometric mean 

and similar triangles to set up two proportions that can be algebraically manipulated 

2 2 2 

to show a + b = c . 

A 

b 

C 

f 

D 

a 

c 

e 

B 

[20]

Geometry B 


Reference: [9.1.1.1] 

[1] 

9 

a = , b = 

2 


15 

2 

[2] a = 10, b = 10 3 , h = 5 3 


[3] 2 19 


[4] 15.652 


[5] 17.5 


[6] B and C 


[7] A. acute triangle, B. right triangle, C. no triangle 


[8] x = 9 2, y = 9 + 9 3 or 9(1 + 3) 


[9] x = 21 3, y = 42 


[10] 4.2 cm

Geometry B 



[11] 

5 

13 


[12] 

5 12 

sin P = , cos P = , tan P = 

13 13 


[13] 2.25 m 


[14] 3 


[15] 11.87 


[16] x ≈ 35 ft 


[17] 6.1 

Reference: [9.7.2.102] 

[18] 〈 – 2, – 3〉 

Reference: [9.7.2.101] 

[19] 〈 1, – 

15〉 

5 

12

Geometry B 



[20] 

Statements 

c a c b 

= and = 

a e b f 

Reasons 

Geometric Mean Theorem 

2 2 

ce = a and cf = b Cross Product Property 

ce + cf = a + b 

c( e + f ) = a + b 

e + f = c 

c = a + b 

2 2 2 

a + b = c 

2 2 2 

2 2 

2 2 

Addition Property of Equality 

Distributive Property 

Segment Addition Postulate 

Substitution Property 

Symmetric Property of Equality

Chapter 9 Test Review with Key

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