Download Geometry Final Exam Review

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Geometry Final Exam Review
The variables r and s represent the lengths of the legs of a right triangle, and t represents the
length of the hypotenuse. Find the unknown value. Then tell whether the lengths form a
Pythagorean triple.
1.
r = 12; s = 16
2. r = 8; t = 12
Decide whether the numbers can represent the sides of a triangle. If they can, classify the
triangle as acute, right, or obtuse.
3. 8, 9, 12
5. The vertices of
acute, or obtuse.
4. 5, 115, 25
are P (2, 3), Q (3, 1), and R (0, 3). Decide whether
is right,
Find the value of each variable.
8.
6.
7.
9.
10. An equilateral triangle has sides of length 18 centimeters. Find the length of an altitude
of the triangle. Then find the area.
Find the sine, cosine, and tangent of the acute angles of the triangle. Express each value as
a decimal rounded to four decimal places.
11.
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Solve the right triangle. Round decimals to the nearest tenth.
13.
14.
12.
15. Complete the following statement: 10, ____, and 26 form a Pythagorean triple.
16. What is the measure of each exterior angle of a regular 30-gon?
17. Find the value of x.
Is PQRS a parallelogram? Explain.
18.
;
19. PR = SQ; PT = TR
20.
and
.
What special type of quadrilateral is shown? Justify your answer.
21.
22.
23. The lengths of the sides of an isosceles trapezoid are 8, 10, 14 and 10. Find the length
of the midsegment.
24. You want to build a plant stand with three equally spaced circular shelves. You want the
top shelf to have a diameter of 6 inches and the bottom shelf to have a diameter of 15
inches. The diagram on the right shows a vertical cross section of the plant stand. What
is the diameter of the middle shelf?
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Use the diagram of
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.
25. Find the lengths of
26. Find the measures of
.
and
.
Find the measure of each numbered angle.
27.
29.
28.
30.
Kite ABCD is inscribed in
reasoning.
31.
and
. Decide whether the statement is true or false. Explain your
are right angles
32.
Find the measure of the arc.
33.
is a diameter, and
°.
34.
35.
Write the standard equation of the circle. Then graph the equation.
36.
Center (–4, –1); radius 4
37.
Center (2, 5); radius 9
38.
Graph the circle with the equation
.
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Use the diagram.
39. Find the circumference and area of
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.
40.
Find the length of
.
41. Find the length of ABC in circle D.
42. Identify the
transformation
.
43. What is the image of
B?
44. What is the preimage
of ?
Describe the composition of the transformations.
45.
46.
47. Identify the dilation, find the scale factor, and find the value of the variable.
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Use the diagram.
48. Identify the transformation
.
49. What is the image of point B?
50. What is the preimage of point
?
Use Euler's Theorem about solids to find the unknown number.
51. Faces: 32
Vertices:
Edges: 90
52. Faces: ____
Vertices: 6
Edges: 10
The two pentagons are similar.
53. Find the perimeter of each pentagon.
54. Find the area of each pentagon.
55. Find the area of the shaded region.
Find the surface area of the right prism.
Round your result to two decimal places.
57.
56.
Find the surface area of the right cone.
Round your result to two decimal places.
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58. Find the volume of the pyramid.
59. Find the surface area and volume of a sphere with radius of 0.5 inch.
60. Find the volume and surface area of a prism with a height of 6 inches and a 4 inch by 4
inch square base. Compare the results with the volume and surface area of a cylinder
with a height of 7.64 inches and a diameter of 4 inches.
61. An equilateral triangle has a height of 6 inches. Find the area of the triangle.
62. Find the surface area of the right cylinder. Round your result to two decimal places.
63. Find the volume of the cone.
64. Find the surface area and volume of a sphere with a radius of 14 meters.
Suppose you are building a silo. The shape of your silo is a right prism with a regular 15gon for a base, as shown. The height of your silo is 59 feet.
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65. What is the area of the floor of your silo?
66. Find the lateral area and volume of the silo.
67. Given: KN || LM
PROVE: KJN ~ LJM
STATEMENTS
REASONS
68. Given: AB ∥ DC
Prove: ABC ~ DCE
STATEMENTS
REASONS