2011-2012 Honors Geometry Final Exam Study Guide

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by

ASA? A. C.

B. D.

____ 2. Which three lengths could be the lengths of the sides of a triangle?

A. 20 cm, 6 cm, 6 cm C. 9 cm, 14 cm, 22 cm B. 14 cm, 6 cm, 20 cm D. 8 cm, 23 cm, 11 cm

____ 3. Which figure is a convex polygon?

A. C.

B. D.

Short Answer

4. Are E, F, and H collinear? If so, name the line on which they lie.

E

F

G

H

5. Name the line and plane shown in the diagram.

O

PM N

6. Name the ray in the figure.

C D

7. If T is the midpoint of find the values of x and ST.

S UT

8x 4x + 20

8. Name an acute angle, an obtuse angle, and a right angle.

P

Q

R

S

T

9. If and then what is the measure of

10. bisects , , . Find .

11. Line r is parallel to line t. Find m 5.

r

t

7

1 3

2

65

4

138°

12. Find the value of the variable if and

1 2

3 4

5 6

7 8

l

m

13. Find the value of k.

80°

40° k °

14. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 44° and the two congruent sides each measure 21 units?

44°

Drawing not to scale

2121

15. Classify the polygon by its sides.

16. ABCD is a parallelogram. If then

A B

D C

17. LMNO is a parallelogram. If NM = x + 13 and OL = 3x + 3 find the value of x and then find NM and OL.

O N

L M

Solve the proportion.

18.

19.

20. Find x so that .

P

Q

R

S

T

, , ,

21. . Complete the statements.

D C

E B

A

J

H

G

F

a.

b. ABGH

DJ

Find the geometric mean of the pair of numbers.

22. 400 and 4

Find the length of the missing side. The triangle is not drawn to scale.

23.

8

6

24.

13

12

25. A triangle has sides of lengths 9, 7, and 12. Is it a right triangle? Explain.

Find the value of x. Round your answer to the nearest tenth.

26.

x

8

Not drawn to scale

Find the value of x. Round to the nearest tenth.

27.

20x

Not drawn to scale

Find the value of x. Round to the nearest degree.

28.

18

9

x

Not drawn to scale

29.

x

11

19

Not drawn to scale

Find each measure using the given measures of . Round measures to the nearest tenth.

30. If 30.4, 24.3, and 15.4, find .

31. In , given the following measures, find the measure of the missing side to the nearest tenth..

, ,

32. Name the minor arc and find its measure.

C

B

A

D )115°

33. Name the major arc and find its measure.

C B

A

D )50°

Use the diagram to find the measure of the given angle.

AB D

C

F

E

50°

34.

35.

36.

Use the diagram to find the measure of the given angle.

R

P

T

S

Q

(3 + 35)°

(4 + 15)°

x

x

37.

Find the measure of the numbered angle.

38.

100°

130°1

39. Find the measure of 8

8

220°

Find x. Assume that any segment that appears to be tangent is tangent.

40.

x°

10° 60°

Find the circumference. Leave your answer in terms of .

41.

7.7 cm

42. Find the perimeter of the rectangle.

35 ft

55 ft

Find the area of the circle. Leave your answer in terms of .

43.

1.9 m

44. Find the area of the shaded region when the circle is removed from the trapezoid.. Dimensions are

in feet. Use 3.14 for .

45. The figure is formed from rectangles. Find the total area.

7 ft3 ft

3 ft

10 ft

Find the area.

46.

5.1 cm

3.8 cm

47. Find the area

15 cm

9 cm

48. Find the area

9 cm

9 cm 11 cm

8 cm

13 cm

49. Find the area.

12.6 in.

29.2 in.

19 in.

14.5 in.

50. The area of a parallelogram is 400 cm2 and the height is 40 cm. Find the corresponding base.

Find the area of the indicated sector(s). Then find the probability of spinning the color indicated if the diameter of the spinner is 12 units.

51. blue

72°72°

72°

72°72°

blue

blue

52. white

white blue

orange

orange orange

44° 90°

46°

48° 47°

43° 42°

blue white

53. Find the probability that a point chosen at random lies in the shaded region.

Find the surface area of the cylinder in terms of .

54.

5 in.

11 in.

Not drawn to scale

Find the surface area of the pyramid shown to the nearest whole number.

55.

4 ft

4 ft

9 ft

Not drawn to scale

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

56.

14 ft

8 ft

4 ft

Not drawn to scale

Find the volume of the cylinder in terms of .

57.

5 in.

10 in.

Not drawn to scale

Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.

58.

18 cm18 cm

12 cm

Not drawn to scale

Find the volume of the cone shown as a decimal rounded to the nearest tenth.

59.

6 yd

14 yd

Not drawn to scale

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.

60.

15 cm

61. An architect designed a circular fountain surrounded by four smaller circular fountains as shown in

the figure. If the diameter of the inner fountain is 12 feet and each of the four surrounding fountains has a diameter of 6 feet, which area is greater, the area of the center fountain or the combined area of the four surrounding fountains?

62. Nick marks the positions of four of the most popular tourist attractions in his city on a map. He finds that the four attractions are located at the vertices of a quadrilateral ABCD. He connects the four points and finds that Find the measure of the angle between the short sides and the angle between the long sides to the nearest degree.

A

B

C

D

Essay

63. A large model of a pencil was constructed for an art show. It consists of two parts: a cone for the

top and a right cylinder for the base, as shown below.

6 in.

6 in.4 in.

12 in.

a. What is the surface area of the cone to the nearest square inch? Use 3.14 for . b. What is the surface area of the cylinder to the nearest square inch? Use 3.14 for . c. What is the surface area of the pencil once it is assembled? Round to the nearest square inch.

Use 3.14 for .