Geometry Semester Review – 2nd Semester
Solve for the each variable.
1.
2.
3. Given the following sides, 20, 21, and 28, classify the triangle as acute, right, or obtuse.
4-8. Solve for each variable below. Leave in reduced radical form.
4.
5.
7.
Semester Review – 2nd Semester
6.
8.
9. Solve the right triangle.
Solve for each variable below.
10.
12.
Find the value of x.
14.
Semester Review – 2nd Semester
11.
13.
15.
16. The measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find
the measure of each angle.
Find the value of each variable in the parallelogram.
17.
18.
19. Three of the vertices of parallelogram JKLM are given.
Find the coordinates of point M.
J(–3, 2), K(4, 2), L(2, 4), M(x, y)
20. Find the value of x.
21. PQRS is a kite. Find m  Q.
Give the most specific name for the quadrilateral.
22.
Semester Review – 2nd Semester
23.
24-25. The vertices of quadrilateral HORS are D(–4, 1), E(–1, 5), F(2, 3), and G(–3, –2). Translate HORS using the
given vector. Graph HORS and its image and label the vertices.
24. 〈2, 3〉
25. 〈–1, –2〉
26. ∆J’K’L’ is the image of ∆JKL after a translation.
Write a rule for the translation and in vector form.
27. Reflect each image over the given line.
y - axis
28-29. Use the graphs below with vertices C(7, -1), A(3, 4), and T(10, 6) to find the coordinates of the vertices of the
triangle when reflected in the given line.
28. x = 4
29. y = - 2
Semester Review – 2nd Semester
30-31. Graph each preimage and image after rotating each figure the given number of degrees about the origin.
30. BEST; B(-3,1), E(-5,2), S(-3,7), T(4,3); 90°
31. MATH; M(1,-2), A(2,8), T(8,0), H(6,-3); 180°
32. a. If possible, draw in all lines of reflection.
b. Does the figure have rotational symmetry? If so, state the angle of rotation.
33. The vertices of ΔCAT are C(– 9, –2), A(–4, 1), and T(–3, –3). Graph each figure using the composition of
transformations given below in the order they are listed.
Translation: (x, y) → (x + 5, y + 1)
Dilation: centered at the origin with k = 2
Graph the equation.
34. (x - 2)2 + (y + 3)2 = 4
Semester Review – 2nd Semester
35. (x + 1)2 + y2 = 16
36. The vertices of ΔBAT are B(– 9, 6), A(–3, 9), and T(6, 3).
Graph each figure using the composition of transformations
given below in the order they are listed.
1
Dilation: centered at the origin with k = 3
Reflection: in the y = –2
̅̅̅̅̅
𝑩𝑫 and ̅̅̅̅
𝑨𝑪 are diameters of circle F. Identify the given arc as a major arc, minor arc, or semicircle. Then find the
measure of the arc.
37. m AB
38. m BC
39. m ACE
40. m BDC
QR is a radius of circle R and PQ is tangent to circle R. Find the value of x.
41.
42.
Write the standard equation of the circle with the given center and radius.
43. Center (–2, -3), radius 7
44. The point (-3,16) is on the circle with center (2,4)
Find the measure of the given arc.
45. m DF
Semester Review – 2nd Semester
46. m JK
In Exercises 47-58, find the value(s) of the variable(s).
47.
48.
50.
51.
52.
53.
54.
55.
56.
57.
58.
Semester Review – 2nd Semester
49.
Find the indicated measure. Round answers to the nearest hundredth.
59. Area of sector ABC
60. Radius of  N
61. Circumference of  Q
In  D shown below, ∠ADC  ∠BDC. Find each indicated measure.
62. m ACB
63. m CB
64. Length of ACB
65. Length of CB
Find the area of the regular polygon. Round answers to the nearest hundredth, if necessary.
66.
67.
68.
Tell whether the solid is a polyhedron. If it is, name the polyhedron, find the number of faces, vertices, and edges.
Explain your reasoning.
69.
70.
71.
Semester Review – 2nd Semester
The area of R is 295.52 square inches. The area of sector PRQ is 55 square inches. Find each indicated measure.
72. Radius of R
73. Circumference of R
74. m PQ
75. Length of PQ
Find the area of the shaded region. Round answers to the nearest hundredth, if necessary.
Then find the probability that a randomly chosen point in the figure lies in the shaded region.
76.
77.
78.
79. Find the volume of a cube is 46,656 cm³. What is the surface area of the cube?
Semester Review – 2nd Semester
80. For the right triangular prism, find:
a. Volume
b. Surface Area
81. The volume of a prism with a square base is 360 cm³, and its height is 10 cm. Find:
a. area of its base.
b. length of a side of the base.
82. Find the surface area of the right square
pyramid to the right.
83. Find the exact volume of the oblique cylinder to the
right.
84. Find the surface area of the cone below.
85. The volume for a cone is 63π cm³. If its radius is 3 cm, what
is its height?
86. Find the surface area and volume of the sphere below.
87. Find the surface area and volume of the cylinder below. (Leave answers in π form.)
Semester Review – 2nd Semester
88. A pyramid has a square base. Its volume is 507 cm³ and the length of a base edge is 13 cm. Find the height of the
pyramid.
89. A pipe is 8 feet long and 1.5 feet wide. How much water would the pipe be able to hold?
90. Two cones have a scale factor of 3 : 7. The smaller cone has a surface area of 169π square yards. Find the surface area
of the larger cone. Write your answer in terms of π.
91. Two spheres have a scale factor of 2 : 5. The smaller sphere has a volume of about 54π cubic meters. Find the volume
of the larger sphere. Write your answer in terms of π.
92. A hexagon has an area of 90 in² with a side length of 5 in. A similar hexagon has a side length of 4 in. What is the area
of the similar hexagon?
93. A swimming pool 10 meters long holds 200,000 liters of water. How much water does a similar pool 15 meters long
hold?
Semester Review – 2nd Semester