18-19 ACP Geometry – Final Exam REVIEW

Chapter 7 – Similarity

1. Given ABC DEF . Find the value of x.

Justify your answer.

Are the following triangles similar? If so, justify your answer, and write a similarity statement.

2.

3.

4. List the ways you can prove two triangles similar.

M

P Q

6

15

N

R S

12

28

5. EKN is similar to OHT . If 49m K and 73Tm , find Em .

6. The triangles are similar. Find the missing side(s) in each figure. Justify your answer.

7. The triangles are similar. Find the missing side(s) in each figure. Justify your answer.

For #8 – 9, the triangles are similar. Find the missing lengths and / or angle measures.

8. 9. 10.

Chapter 8 – Right Triangles (Geo Mean, Pythagorean, Special Right, and Trig)

.

11. Can the 6, 8 and 27 be the lengths of the sides of a triangle? Explain why or why not.

12. Find the geometric mean of the following, rounded to the nearest tenth.

a) 6 and 18 b) 7 and 125 c) 9 and 36

13. 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.

G M

START

CUP

x y

14. Joan places a mirror 24 ft from the base of a tree. When she stands 3 ft from the mirror, she can see the top

of the tree reflected in it. If her eyes are 5 ft above the ground, how tall is the tree? (Draw the situation

described and explain why the triangles are similar)

Find the length of the missing side. Leave your answer in simplest radical form.

15.

Find the missing values.

16. 17.

18. Find the length of the hypotenuse.

19. Find the length, d, in simplest radical form, of the diagonal of a cube with sides of s units.

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

20. 21.

Find the area of the trapezoid. Leave your answer in simplest radical form.

22.

Write an equation involving sine, cosine, or tangent that can be used to find x. Then, solve the equation.

Round answers to TWO decimal places.

23. 24. 25.

26. 27. 28.

29. If the 5

tan( )12

A what is the cos( )?A

30. To approach runway 17 of the Ponca City Municipal Airport in Oklahoma, the pilot must begin a 3°

descent starting from an altitude of 2714 ft. The airport altitude is 1007 ft. Create a trigonometric equation to

find how many miles the airplane is from the runway, and then find that distance, to the nearest foot.

21

x5

54 x

1033

5.2

x

17

x

41 x

5

8 x

8

5

Chapter 9 - Circles

1. If the circumference of a circle is 51in what is the radius? Round your answer to the nearest tenth.

2. If the area of a circle is 2100 cm , then what is the radius?

Find the area of the shaded region in each circle below, using 3.14 for π. Round to the nearest tenth.

3. 4. 5.

6.

Find the length of AB in each circle using the pi button on your calculator. Round to the nearest tenth.

7. 8.

3in

707 in

155

8in

120 80

5in

4in

60

22in

60

Find the length of ABC in each circle using 3.14 for π. Round to the nearest tenth.

9.

Assume that the lines that appear to be tangent are tangent. Find the value of x.

10. 11.

Each polygon is circumscribed about the circle. Find the perimeter of each polygon.

12. 13.

12 in

120

x

52

5

x

9cm 12cm

8cm7cm

15in

18in

13in

6in

4in

8

Find the value of x. If necessary, round to TWO decimal places.

14. 15. 16.

Find the value of each variable. If necessary, round to TWO decimal places. Justify your answer.

17. 18. 19.

For 20-22, write the standard equation of each circle.

20. C(2, -7); r = 7 21. C(-10, -5); passes through the point (-5, 5)

15

12x x

9924

x

6.6

2.13

5

97

x

58

23

x

y

x

y

w

67

86

162

22.

23. Write the standard equation of the circle, and identify its radius and center.

𝑥2 + 𝑦2 + 12𝑥 − 4𝑦 − 8 = 0

24. Identify the center and radius of the following:

2 2( 5) ( 9) 72x y

Chapter 10 – Area and Surface Area

1. Find the value of h in the parallelogram.

Not drawn to scale

2. The area of a square garden is 50 m2. How long is the diagonal?

3. A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?

4. Find the area of the rhombus.

4cm

Find the area of the following shapes.

5. 6.

7.

8. Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle.

Leave your answer in terms of .

8in

5

9

7

Find the area. The figure is not drawn to scale.

9.

10. 11.

12. A room is 14 ft long and 28 ft wide. The ceiling is 8 ft high. A particular brand of paint will cover 125 ft2

per gallon. How many gallons of paint are needed to paint the walls of the room?

13. Find the Lateral area and Surface area of the following figures:

LATERAL AREA ONLY!!!

14. Find the surface area of the sphere with a diameter of 16 cm, in terms of π.

Chapter 11 – Volume

Find the volume of the given prism. Round to the nearest tenth if necessary.

1. 2.

3. Find the volume of the cylinder in terms of π.

Find the volume of the following figures, to the nearest whole number.

4. 5. 6.

Find the volume of the following spheres. Give each answer rounded to the nearest cubic unit.

7. 8.

9. Find the volume of the cube after the cone was drilled out of it.

10. Josh has a cylindrical pool with a diameter of 22 feet and a height of 6 feet. He fills it with water until it is

six inches from the top of the pool. If 1 3ft = 7.48 gallons and water costs $.009 per gallon, how much did Josh

spend filling his pool?