Download semester2 final examination review for geometry cp1

SEMESTER2 FINAL EXAMINATION REVIEW FOR GEOMETRY CP1.
1. ABCD is a rectangle. m  AED = 64  . Find the measure of  CBD.
D
C
E
B
A
___________
2. Find the value of x and y if the quadrilateral is a rectangle.
A. x = 11 and y = 7
B. x = 7 and y = 22 C. x = 7 and y = 11
D. x = 22 and y = 11 E. x = 22 and y = 7
14y
___________
154
23x - 7
3. Which of the following statements is true ?
A. If a quadrilateral has a right angle, then the quadrilateral is a rectangle.
B. If a quadrilateral is a rectangle, then its diagonals are perpendicular.
C. If a quadrilateral has opposite sides that are congruent, then the quadrilateral
is a rectangle.
D. If a quadrilateral is a rectangle, then opposite angles are congruent.
___________
4. ABCD is a rhombus. m  BAC = 30  and DC = 32. Find the measure of DE .
C
D
B
A
___________
5. Given trapezoid ABCD with median EF . If EF = 23 and DC = 30, find AB.
A
E
D
B
F
C
___________
6. J and M are base angles of an isosceles trapezoid JKLM. If m J = 20x + 6,
and m M = 16x + 7, find the value of x.
A. – 2 B. ¼ C. – ½ D. 13/4
___________
x x2

20
30
7. Solve for x.
_____________
8. The measures of the corresponding sides of the polygons are proportional. If
AD = 6, DC = 2, and WZ = 9, find YZ.
X
B
W
C
A
Y
D
Z
_________
A
D
10
y
9.
ABC
DEF. Find x and y.
B
C
6
x
8
F
E 4
x = _______
y = ________
A
P
9
6
Q
18
10. PQ // BC . Find the measure of AB .
11.
ABC
XYZ . If the perimeter of
B
C
___________
ABC is 22.75, find the perimeter of XYZ .
Y
B
3
6
X
Z
A
C
___________
12. Find the geometric mean of 12 and 10 in lowest square root form.
___________
Solve the following problem for x.
x
13.
3
9
____________
x
3.3
15. Solve for x.
40
5
14. Solve for x.
______________
x
5.6
______________
16. Classify a triangle with sides of 30, 24 5 and 20 10 as acute, right,
or obtuse. EXPLAIN YOUR WORK !
17. Determine if the measures 15, 12 , and 20 are measures of the sides of a right
triangle. EXPLAIN YOUR WORK !
18. In EFG , E is a right angle and m F = 45  . If EF = 30 feet, find FG. _________
x
2
60
y
19. Find the value of x and y.
x = __________
y = __________
20. A ladder,12 feet tall, makes an angle of 32  with the ground. If it is leaning
against a wall, how high is the top of the ladder above the ground ?
_________
6x + 8
9x - 16
21. Solve for x.
___________
22. You are standing at point B which is 40 feet from the center of a circular water
bin and 25 feet from point A. Find the radius of the bin.
A
B
O
_________
C
O
B
A
23. m BAC = 280  . Find m  B .
_________
24. Find m ABC if m ABC = 3y – 6 and m ADC = y + 40.
A
B
C
D
_________
A
O
25. m C = 38  . Find m AOB .
26.
B
C
__________
m ABE = 100  and m DCF = 110  . Find the degree measure of each angle.
1 = _______ 2 = _________
3 =_______ 4 = _________
B
1
A
E
3
C
2
D
4
F
27. m BA = m AE . m BD = 30  and m DE = 120  , find m ACE .
A
B
C
D
E
_________
B
A
x
D
C
28. m AB = 32  and m CD = 64  . Find x.
_____________
29. CB = 30 and DB = 20. Find the diameter of the circle.
A
O
C
D
B
_____________
30. Circle 0 with radius 20. OC = 12. Find AB.
C
A
B
O
_____________
31. AC is the diameter of circle O. m AOB = 136  . Find m BAC .
A
O
C
B
_____________
C
B
32. m ABC = 262  . Find m CDA.
D
A
_____________
33. AB is the diameter of circle O. m BC = 46  . Find m CAB .
C
A
O
B
______________
34.
AB is tangent to circle C at point B. AB = 15 and AC = 17. Find BC.
B
A
C
__________
10 9
x
21
35. Find x.
__________
36. Write the equation of a circle with center ( 2 , - 5 ) and radius 8 2 .
________________
37. Find the sum of the measures of the interior angles of an octagon. _______________
38. Find the sum of the measures of the interior angles of a pentagon. ________________
39. Find the sum of the measures of the interior angles of a decagon. ________________
40. Find the measure of one interior angle and one exterior angle of a regular
hexagon.
interior angle _______
exterior angle_______
63 feet
54
47
41. Find the area of the parallelogram.
_______________
12
8
42. Find the area of the triangle.
( answer in lowest square root form).
_______________
B
A
43. Find the area of the rhombus.
C
D
AB = 10 and AC = 12
_________
44. Find the circumference and area of a circle with a diameter of 12 meters.
C = __________
A= __________
45. A circle has a circumference of 22  meters. Find its area. Leave in pi form.
_________
46. Find the area of an equilateral triangle with a side of 20 cm. Find its altitude.
Area = _______
Altitude=_______
47. Find the area of a hexagon with a side of 10 meters.
________
48. Find the area of a regular heptagon with a side of 10 cm.
________
49. Find the area of a regular octagon with a radius of 10 cm.
________
50. The ratio of the side lengths of 2 regular octagons is 5 to 8. If the area of the
smaller octagon is 20 sq. units, find the area of the larger octagon.
_________
51. Find the length of a 36  arc in a circle with a radius of 6. Leave in pi form.
___________
A
89
4 cm. B
52. Find the area of the sector.
___________
53. Each circle has a radius of 2 inches. Find the area of the shaded region for
square ABCD. Leave answer in pi form.
A
B
D
C
_____________
54. The radius of the circle is
6 . The distance from the center to the chord is
A
C
B
O
3 . Find the area of the shaded region. Leave in pi form.
__________
55. According to a survey, 20 out of every 25 students do not walk to school.
Find the ratio of walkers to total students.
___________
56. In the figure (not drawn to scale), the hexagon ABCDEF is similar to hexagon
JKLGHI. Find the length of BC to the nearest 10th. KL = 14 , CD = 8 and LG = 17.
__________
J
A
F
B
E
C
K
L
I
H
D
G
57. Mr. Jones has taken a survey of college students and found that 50 out of 56
students are liberal arts majors. If a college has 10,067 students, what is the
best estimate of the number of students who are liberal arts majors ?
A. 8988
B. 56
C. 89,884 D. 11,275 E. 5,034
____________
58. If two polygons are similar, then corresponding angles are:
A. complementary B. congruent C. supplementary
D. a linear pair
_______
59. From a point 65 feet from the base of a tree, the angle from ground level to the
top of the tree is 37  . Find the height of the tree to the nearest foot.
________
8 cm.
60. Find the area of the regular pentagon.
_________
61. How far from the center of a circle of radius 15 is a chord of 18 ?
_________
16
26 m
62. Find the surface area.
12
___________
10
8
15
63. Find the surface area.
___________
64. Find the surface area and volume. Diameter = 4 meters.
S.A.=___________
V=___________
6.8 m
___________
6 feet
4
65. A square pyramid. Find the surface area.
___________
66. Find the volume of a cone(draw it) with a height of 30 inches and a radius of 5 in.
( leave answer in terms of pi).
___________
11 meters
67.
16
12
Find the volume.
___________
13 feet
68.
Find the volume.
(square pyramid)
6
__________
10
meters
4
69.
Find the surface area.
____________
70.
Find the surface area and volume of a sphere with a diameter of 20 feet.
( leave answer in pi form).
S.A.=__________
V=___________
71. A pyramid has a square base and 4 triangular faces that are congruent.
AB = 4. Surface area = 80 sq. inches. Find the slant height, CD, in inches.
D
E
A
C
B
______________
72. Two similar solids have a scale factor of 2 to 3. If the smaller solid has a
surface area of 200 square meters, find the surface area of the larger solid.
______________
73. Two similar solids have a scale factor of 3 to 5. The larger solid has a volume
of 1000 cubic feet. Find the volume of the smaller solid..
_____________
74. The center of a circle is ( - 3 , 0 ) and its radius is 5. Which point is not on the
circle ?
A. ( 2 , 0 ) B. ( 0 , 4 ) C. ( - 3 , 0 ) D. ( - 3 , - 5 ) E. ( - 8 , 0 )
_________
75. Draw a cylinder. A cylinder has a height of 15 inches and a diameter of 10 in.
How many gallons of water will it hold if 1 gallon of water = 231 cubic inches ?
_________
2
4
76. 2 cubical containers.
If the smaller cube is completely filled with water, and all the water is poured into
the larger cube, what will be the height of the water in the larger cube ?
_________
77. A rectangular swimming pool has dimensions 15 feet by 12 feet by 10 feet.
How many gallons of water are needed to fill the pool if 1 cubic foot = 7.48
gallons of water ?
_________
78. Solve the right triangle using trigonometric functions. Angles to the nearest
whole degree.
C
6
B
10
A
 A = __________
 B = __________
AC = _________
79. The perimeter of a rectangle is 80 meters. The ratio of its sides is 3 : 5.( width to length).
Find the length of its sides.
_________ and _________