GRE_Math_Bible_eBook
.pdf
Geometry 91
7.In the figure, what is the value of a ?
(A)16
(B)18
(C)36
(D)54
(E)72
2a° 3a°
a° 4a°
l
8.In the figure, what is the average of the five angles shown inside the circle?
(A)36
(B)45
(C)60
(D)72
(E)90
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(2a – 2b)°
9.In the figure, O is the center of the circle. What is average of the numbers a, b, c, and d ?
(A)45
(B)60
(C)90
(D)180
(E)360
a° b° d° Oc°
92 GRE Math Bible
10. |
Column A |
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The perimeter of ∆ABC |
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The circumference of the circle |
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11. |
Column A |
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Column B |
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The perimeter of quadrilateral |
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The circumference of the circle |
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ABCD |
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12. |
Column A |
A circle is inscribed in a triangle. |
Column B |
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The perimeter of the triangle |
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The circumference of the circle |
Medium |
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13. |
Column A |
In ∆ABC, B = 72° |
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Geometry 93
14.In the figure, AD and BC are lines intersecting at O. What is the value of a ?
(A)15
(B)30
(C)45
(D)60
(E)135
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5x + 5a |
2x + 30 |
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B
15.From the figure, which one of the following must be true?
(A)y = z
(B)y < z
(C)y ≤z
(D)y > z
(E)y ≥ z
y z x 3x
94GRE Math Bible
16.From the figure, which one of the following could be the value of b ?
(A)20
(B)30
(C)60
(D)75
(E)90
a° |
b° – a°/2 |
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2a° – b° O a°/2 + 2b°
2a° – 2b°
17. AD is the longest side of the right triangle ABD shown in the figure. What is the length of longest side of ∆ABC ?
(A)2
(B)3
(C)
41
(D)9
(E)41
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4
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The figure is not drawn to scale
Geometry 95
18.In the figure, what is the value of a ?
(A)30
(B)45
(C)60
(D)72
(E)90
l |
m |
3c°
6c° 2b°
a° b°
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19.In the figure, lines l and m are parallel. Which one of the following, if true, makes lines p and q parallel?
(A)a = b
(B)a = c
(C)c = d
(D)d = b
(E)b = c
p q
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a° b° |
c° d°
m
20.A, B, C, and D are points on a line such that point B bisects line AC and point A bisects line CD. What is the ratio of AB to CD ?
(A)1/4
(B)1/3
(C)1/2
(D)2/3
(E)3/4
21.If A, B, C, D, and E are points in a plane such that line CD bisects ACB and line CB bisects right angle ACE, then DCE =
(A)22.5°
(B)45°
(C)57.5°
(D)67.5°
(E)72.5°
96 GRE Math Bible
22.From the figure, which of the following must be true?
(I)x + y = 90
(II)x is 35 units greater than y
(III)x is 35 units less than y
(A)I only
(B)II only
(C)III only
(D)I and II only
(E)I and III only
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35°
x° y°
m
23.In the figure, triangles ABC and ABD are right triangles. What is the value of x ?
(A)20
(B)30
(C)50
(D)70
(E)90
B
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x° |
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Geometry 97
24.In the figure, ABC is a right triangle. What is the value of y ?
(A)20
(B)30
(C)50
(D)70
(E)90
B
y°
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25.The following are the measures of the sides of five different triangles. Which one of them represents a right triangle?
(A)
3 , 
4 , 
5
(B)1, 5, 4
(C)7, 3, 4
(D)
3 , 
7 , 
4
(E)4, 8, 10
26.∆ABC is a right-angled isosceles triangle, and B is the right angle in the triangle. If AC measures
7
2 , then which one of the following would equal the lengths of AB and BC, respectively?
(A)7, 7
(B)9, 9
(C)10, 10
(D)11, 12
(E)7, 12
98 GRE Math Bible
27.In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =
(A)12
(B)13
(C)15
(D)17
(E)24
A
8
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28.The average length of the sides of ∆ABC is 12. What is the perimeter of ∆ABC ?
(A)4
(B)6
(C)12
(D)24
(E)36
A
60°
B C
29.Which one of the following is true regarding the triangle shown in figure?
(A)x > y > z
(B)x < y < z
(C)x = y = z
(D)2x = 3y/2 = z
(E)x/2 = 2y/3 = z
z°
B
1 1/2 |
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x° A |
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C y° |
Geometry 99
30.In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What is the area of the rectangle?
(A)18
(B)22.5
(C)36
(D)44
(E)45
A
B
4
E
5
D C
31.In the figure, what is the area of ∆ABC ?
(A)2
(B)
2
(C)1
(D)
1
2
(E) 1/2
2z°
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100GRE Math Bible
32.In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?
(A)Always less than 10
(B)Always greater than 40
(C)Always greater than 30
(D)Always less than 30
(E)Less than 40 and greater than 20
O
10
B
A
33.Which of the following must be true?
(I)The area of triangle P.
(II)The area of triangle Q.
(III)The area of triangle R.
(A)I = II = III
(B)I < II < III
(C)I > II < III
(D)III < I < II
(E)III > I > II
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