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GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET For 1–2, use the graph. 1. Which segment is congruent to ______________________________________ 2. What is the midpoint of ______________________________________ Use the following information for 3–4. In the figure, 3. What is the value of x? _______________________________ 4. What is mKJM ? _______________________________ 5. Line segment PQ with endpoints P(4, 2) and Q(2, 0) is rotated 90° clockwise around the origin. What are the coordinates of the midpoint of ______________________________________ 6. State the converse of the statement. Then determine whether the converse is true. Explain. If two angles are vertical angles, then they are congruent. ______________________________________ ______________________________________ ______________________________________ 7. Use the graph. Write the vector that maps RST to RST. ______________________________________ Use the figure for 8–9. 8. How many lines of symmetry does the figure have? ______________________________________ 9. What are the angles of rotation less than 360 for the figure? ______________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 1 NAME DATE PER:
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GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET
For 1–2, use the graph.
1. Which segment is congruent to _________________________________________
2. What is the midpoint of _________________________________________
Use the following information for 3–4.
In the figure,
3. What is the value of x?__________________________________
4. What is mKJM?__________________________________
5. Line segment PQ with endpoints P(4, 2) and Q(2, 0) is rotated 90° clockwise around the origin. What are the
coordinates of the midpoint of _________________________________________
6. State the converse of the statement. Then determine whether the converse is true. Explain.If two angles are vertical angles, then they are congruent.___________________________________________________________________________________________________________________________
7. Use the graph.
Write the vector that maps RST to RST. _________________________________________
Use the figure for 8–9.
8. How many lines of symmetry does the figure have?_________________________________________
9. What are the angles of rotation less than 360 for the figure?_________________________________________
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Name_________________________________________ Date____________________ Class___________________
Use the following information for 10–11.
In the figures below,
10. What is the value of x?
_________________________________________
11. What is the value of y?
_________________________________________12. In the figure, m2 75.
What is m7?
13. The measures of two complementary angles are represented by the expressions (3x 16) and (5x 18) Find the value of x.
_________________________________________
14. Write an equation for the line that passes through (1, 3) and is perpendicular to
_________________________________________
15. Write an equation for the line that passes through (3, 2) and is parallel to 2x 3y 3.
_________________________________________
16. In the figure, the measure of 2 is 55.
What is the measure of 4?_________________________________________
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Name_________________________________________ Date____________________ Class___________________
17. Use the figures.
Determine the value of x that ensures that the triangles are congruent._________________________________________
For 18-19, state the additional congruency statement or statements needed to prove
for the given theorem.
18. ASA Theorem_________________________________________
19. AAS Theorem _________________________________________
20. Look at the figure below.
Are triangles DEF and FGH congruent? Explain why or why not. If the triangles are congruent, write a congruence statement._________________________________________
_________________________________________
21. In the figure,
Explain why __________________________________________________________________________________
22. In the figure, mBAC (9x 4)° and mBAD (3x 8) °.
What value of x indicates that is the angle bisector of _________________________________________
23. Use the figure.
What is the value of x?_________________________________________
24. The sum of the measures of the interior angles of a regular polygon is 900. How many sides does the polygon have? _________________________________________
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Name_________________________________________ Date____________________ Class___________________
25. Triangle RST is an isosceles triangle with mR 120. What is mS? Explain your reasoning.__________________________________________________________________________________
26. The sides of a triangle measure 5 meters and 8 meters. What are the possible side lengths for the third side? Show your work.
__________________________________________________________________________________
For 27-28 use the figure.
27. If EG 4, what is GC? _________________________________________
28. If AF 15, what is AG? _________________________________________
29.In the figure, is the midsegment of
If KM 11 cm and KL 24 cm, what is KN?_________________________________________
30. In the figure, and are perpendicular bisectors.
If LP 5, LH 12, HP 13, and PM 6, what is PJ?
_________________________________________
31. ABCD is a quadrilateral with and BCD DAB.
If EC 16 cm, mABC 64, AE 3x 5, and mDAB (4y 12), for what values of x and y is ABCD a parallelogram?
__________________________________________________________________________________
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32. State whether each quadrilateral has congruent diagonals.A parallelogram Yes
NoB rhombus Yes
NoC rectangle Yes
NoD isosceles trapezoid Yes
NoE kite Yes
No
33. GIJL is a trapezoid with midsegment
If IJ 18 cm and GL 42 cm, what is HK?
__________________________________________________________________________________
34. Triangle PQR is shown in the graph.
Classify the triangle. Explain your reasoning.__________________________________________________________________________________
35. A parallelogram has vertices D(4, 1), E(2, 5), F(4, 3), and G(2, 3). Determine whether DEFG is a rhombus, rectangle, or neither. Explain your reasoning.
__________________________________________________________________________________
The figure is symmetric about the x-axis.
36. Find the perimeter of the figure. Round to the nearest tenth.
_________________________________________
37. What is the area of the figure?
_________________________________________
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Name_________________________________________ Date____________________ Class___________________
Use the following information for 38-39.Triangle ABC has vertices A(6, 2),
B(2, 2), and C(4, 8). Dilate using
a factor of about the origin. Then dilate its image using a scale factor of 5 about the origin.38.Determine the coordinates of the final
image. _________________________________________
39. Determine the scale factor you could use
to dilate about the origin that would result in the final image in one step._________________________________________
40. maps to with the transformation
If CD 9, what is LM?_________________________________________
Use the following information for 41-42.Polygons BCDE and FGHI are similar.41. Write a proportion that contains BE
and CD._________________________________________
42. List any angles that are congruent to
__________________________________
43. If CD 8, FG 12, and GH 24, what
is the length of _________________________________________
Use the figure for 44-45.
44. Which triangles are similar? Write a similarity statement._________________________________________
45.What is AB? _________________________________________
46.Use the figure to find the unknown distance.
What is the distance across the river?
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Name_________________________________________ Date____________________ Class___________________
47. Rectangles ABCD and EFGH are similar. Rectangle ABCD has a length of 20 cm and a perimeter of 60 cm. Rectangle EFGH has a length of 32 cm. Find the area of rectangle EFGH.
_________________________________________
Use the following information for 53–55.In the figure, PS 4 and SQ 16. Find each length to the nearest tenth.
48.What is the length of _________________________________________
49.What is the length of _________________________________________
50.What is the length of _________________________________________
51.Use the figure.
What is the length of __________________________________________________________________________________
Use triangle XYZ for 52-53. Round to the nearest tenth.
52. What is YX?
_________________________________________
53. What is YZ?
_________________________________________
Use the triangle below for questions 54-55. Round to the nearest tenth.
54. If and b 15 cm, what is a?
_________________________________________
55.If a 12 cm, b 18 cm, and c 8 cm, what is _________________________________________
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56. In the figure, mKJL (12x 8) and mKML (10x 16) °.
What is the value of x?_________________________________________
57 In the circle, and
What is mV? _________________________________________
Use the circle for 58-59.In the circle, and
58.What is mAED? __________________________________
59.If DE 3, EB 16, and AE 4, what is EC?
_________________________________________
Use the circle for 60-62.
60. Find the exact arc length of .
_________________________________________
61. Convert the central angle to radians.
__________________________________
62. What is the area of the sector formed by RPQ to the nearest tenth?
_________________________________________
63. Write an equation of a circle with center (3, 4) and radius 2.
__________________________________
64. Find the center and radius of the circle with the following equation.
_________________________________________
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Use the information for 65-66. A prism has 6-inch square bases and a height of 10 inches. A cylinder has a diameter of 10 inches and a height of 6 inches. 65. Which solid has the greater volume?
_________________________________________
66. Which solid has the greater surface area?
_________________________________________
67. The oblique cylinder shown below has a volume of 36 cubic inches. What is the radius of the base of the cylinder to the nearest tenth of an inch?
_________________________________________
68. A right cone has a slant length of 9 centimeters and a radius of 4 centimeters. What is the surface area of the cone? Round to the nearest tenth of a square centimeter.
_________________________________________
69. The triangular prism has a surface area of 510 square meters. Find the missing value for x.
DIAGRAM IS AT TOP OF NEXT COLUMN
_________________________________________70.A square pyramid and a cube have equal
volumes. The side length of the base of each figure is 16 millimeters. How many times taller is the pyramid than the cube?_________________________________________
71. A cylinder has a radius of 8 inches and a height of 16 inches. The radius of a cone is half the length of the radius of the cylinder. If the cylinder and the cone have equal volumes, how many times greater is the height of the cone than the height of the cylinder? _________________________________________
Use the following information for 80–81. A company sells several sizes of the same design of trash cans. The trash cans consist of a cylinder and a hemisphere. The smallest size trash can has the dimensions shown.
72.What is the volume of the trash can to the nearest tenth of a cubic inch?_________________________________________
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