Download ExamView - Geometry Semester 2 Review.tst

Name ___________________________________________________ Period ______
Geometry Semester 2 Review
1. The shorter leg of a 30°-60°-90° triangle is 8.5 feet long. Find the perimeter.
2. An equilateral triangle has side lengths of 7. The length of its altitude is _____.
3. A photographer shines a camera light at a particular painting forming an angle of 40° with the camera platform. If
the light is 58 feet from the wall where the painting hangs, how high above the platform is the painting?
4. Write cos B.
5. Which of the following is NOT enough information to solve a right triangle?
a. Two sides
b. One side length and one trigonometric ratio
c. Two angles
d. One side length and one acute angle measure
6. The measure of each interior angle of a regular hexagon is ________.
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7. The measure of each exterior angle of a regular octagon is ______.
8. Find the measure of one of the exterior angles of a regular polygon with nine sides.
9. Find the value of x.
10. Find the measure of an interior angle and the measure of an exterior angle for the regular polygon.
16-gon
11. Find each unknown angle measure.
12. Consecutive angles in a parallelogram are always ________.
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13. If ON = 7x − 5, LM = 6x + 3, NM = x − 4, and OL = 2y + 5, find the values of x and y given that LMNO is a
parallelogram.
a.
b.
1
13
;y=
2
2
x = 8; y = −2
x=
c.
d.
1
2
x = 2; y = −2
x = 8; y = −
14. Choose the statement that is NOT always true.
For an isosceles trapezoid _______.
a. the diagonals are congruent
b. the base angles are congruent
c. the diagonals are perpendicular
d. the legs are congruent
15. Choose the figure below which satisfies the definition of a kite.
a.
c.
b.
d.
16. The coordinates of quadrilateral PQRS are P(–3, 0), Q(0, 4), R(4, 1), and S(1, –3). What best describes the
quadrilateral?
17. Use slope or the Distance Formula to determine the most precise name for the figure: A(–1, –4), B(1, –1), C(4, 1),
D(2, –2).
18. If all four sides of a quadrilateral are congruent, the quadrilateral is _______.
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19. Which of the following transformations represents an isometry?
c.
a.
b.
d.
20. The point A(4, -5) is translated onto A′ by the vector u
ç = 〈7, − 3〉. The coordinates of A′ are _______.
21.
Segment AB is translated so that (x, y)→ (x + 4, y – 3).
Find the coordinates of the endpoints of the image A′B ′.
ÈÍ
ÍÍ −3
ÍÍ
ÍÍ
22. If A = ÍÍÍÍ −6
ÍÍ
ÍÍ −9
ÍÍÎ
7
−7
ÈÍ
ÍÍ
Í 0
23. Subtract. ÍÍÍÍ
ÍÍ
ÍÎ −2
7
˘
−2 ˙˙˙˙
˙˙
˙
5 ˙˙˙˙ and B =
˙˙
0 ˙˙˙˙
˚
˘˙ ÈÍ
˙ Í
9 ˙˙˙˙ ÍÍÍÍ −6
˙˙ – ÍÍ
˙ Í
4 ˙˙˚ ÍÍÎ −6
ÈÍ
ÍÍ −2
ÍÍ
ÍÍ
ÍÍ −5
ÍÍ
ÍÍ
ÍÍ −7
ÍÍÎ
2
3
−9
˘
7 ˙˙˙˙
˙˙
˙
−4 ˙˙˙˙ , find A + B.
˙˙
−3 ˙˙˙˙
˚
˘˙
˙
−9 ˙˙˙˙
˙˙
˙
−5 ˙˙˚
4
ÈÍ
ÍÍ
Í −9
24. Multiply. ÍÍÍÍ
ÍÍ
ÍÎ −7
˘˙ ÈÍ
˙Í
−5 ˙˙˙˙ ÍÍÍÍ 5
˙˙ ÍÍ
˙Í
3 ˙˙˚ ÍÍÎ 4
˘˙
˙
−2 ˙˙˙˙
˙˙
˙
7 ˙˙˚
25. Graph the triangle whose vertices have the coordinates given below. Then draw its reflection in the x-axis.
(–7, 2), (–2, 2), (–6, 7)
26. Use the graph below to complete the sentence.
Figure A′B ′C ′D ′ is the image of figure ABCD under a rotation _______
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27. The transformation ÊÁË x, y ˜ˆ¯ → ÁÊË −x, − y ˜ˆ¯ is applied to the figure below. Graph the image of the figure under this
transformation.
28. The composition of two (or more) isometries is always ______.
29. How many lines of symmetry does an isosceles right triangle have? Draw a diagram to illustrate.
30. Is it possible to sketch an isosceles trapezoid with exactly two lines of symmetry?
31. AB is tangent to ñO at A (not drawn to scale). Find the length of the radius r, to the nearest tenth.
32. Given: In ñO, mBAC = 290°. Find m∠B.
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33. Find the measure of DBC in ñP .
34. If QT and RW are diameters in ñ P , find m QW .
35. Given: m∠IED = 116° and m∠JFG = 100°
Find the measure of each unknown angle. (not drawn to scale)
36. Use the diagram (not drawn to scale) and the given information.
mBCD = 111°, mDEF = 100°, mFGH = 127°, and mHAB = 22°
Find m∠FPD.
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37. m AB = 93°, mCD = 27°
Find m∠DOC.
38. Use the diagram (not draw to scale) and the given information.
Find the value of x if m AB = 59° and mCD = 47°.
39. Find the value of x.
40. Find the value of x.
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2
2
41. Sketch the graph of the equation (x − 2 ) + ÊÁË y + 1 ˆ˜¯ = 13. Label the coordinates of the center and the y-intercepts.
42. The standard equation of a circle with center (–4, 3) and radius 7 is _____.
43. A rectangular garden, 42 feet by 20 feet, is surrounded by a walkway of uniform width. If the total area of the garden
and walkway is 1248 square feet, the width of the walkway is _______.
44. The area of the parallelogram is _____.
45. Find the area of the region shown by dividing it into two trapezoids.
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46. The ratio of the side lengths of two regular hexagons is 4 to 9. If the area of the smaller hexagon is 16 square
units, then the area of the larger hexagon is _____.
47. If a circle has a diameter of 7 inches, what is the circumference rounded to the nearest whole number? Use π ≈ 3.14.
48. For a circle of radius 4 inches, find the length of an arc s with a measure of 20°.
49. An automobile has 20-inch diameter wheels. If the wheels revolved three times after the brakes were applied, the
stopping distance was approximately _____.
50. In this figure, each circle has a radius of 2 inches. What is the area of the portion outside the circles but inside the
square? Express your answer in terms of π.
51. Each circle is tangent to the other two. If the diameter of the large circle is 12, the area of the shaded region is
_____.
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52. The circle graph below shows the main sources of water pollution in a county.
What is the measure, in degrees, of the central angle of the section of the circle that represents the pollution
caused by industry?
53. Find the area of the shaded sector in terms of π.
54. A regular hexagon has an apothem of 2 and a side length of
11
4 3
. Its area is _____.
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55. Half of a circle is inside a square and half is outside, as shown. If a point is selected at random inside the square,
find the probability that the point is also inside the circle.
56. The surface area, in square centimeters, of the right cylinder below is _____.
57. A planar cross section that is perpendicular to both bases of a right circular cylinder is a rectangle. What is the shape
of a planar cross section that is parallel to the bases of the same cylinder?
58. Find the surface area of the regular pyramid below.
59. Find the surface area of the right cone shown. (Round the result to two decimal places.)
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60. Find the volume of the right triangular prism.
61. Find the volume of a cylinder with height 9.7 km and diameter 20 km. Use π ≈ 3.14.
62. A cylindrical can is 20 cm in diameter and 16 cm in height. You want to reduce the diameter of the can to 16 cm.
What must the height be if the new can still has the same volume? Explain your answer.
63. Calculate the volume of a cone with height 5 feet and radius 6 feet. Express in terms of π.
64. What is the volume of a sphere with diameter 9.4 feet?
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