Download Objective 1

8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
1) An inflated round balloon with radius r = 50 centimeters holds approximately 523,600 cubic
centimeters of air. When the balloon is contracted such that the radius is 2/3 the original size, what is
the approximate volume of the partially deflated balloon?
A
1.94 x 104 cm3
B
1.55 x 105 cm3
C
1.75 x 105 cm3
D
3.49 x 105 cm3
2) Given: k || m || n. Which statement justifies the conclusion that 1  2  3 ?
A
If k || m || n and are cut by transversal t, then alternate interior
angles are congruent.
B
If k || m || n and are cut by transversal t, then vertical angles
are congruent.
C
If k || m || n and are cut by transversal t, then alternate exterior
angles are congruent.
D
If k || m || n and are cut by transversal t, then corresponding angles are congruent.
3) In the diagram, GH || IJ . If mGLK  55 and mEFJ  120 , what is mKEF ?
A
55º
B
60º
C
65º
D
70º
4) ABCD is a parallelogram. If mBCD  6 x  20 º and mDAB  2x  80 º, what is the value
of x?
A
1
8.3
B
12.5
C
15
D
25
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
5) Given RS || TU , m7  (3x  10) and m3  (2 x  5) . What is m1?
A
15º
B
35º
C
75º
D
145º
6) XYZ shown below has a measure of (8x + 12)º. The measure of 1 is (4x + 8)º and the measure
of 2 is (9x – 11)º. What is the measure of XYZ ?
A
3°
B
20°
C
36°
D
60°
7) In the drawing, what is the measure of angle y?
A
40°
B
60°
C
80°
D
100°
8) Given: m1  4x º, m2  3x  10 º, and m3  2x  17 º. What is m2 ?
2
A
17º
B
31º
C
47º
D
61º
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
9) In the figure below, 1 is supplementary to 3 under which of the following conditions?
A
Line a is parallel to line b.
B
Line a is parallel to line c.
C
Line a is perpendicular to line c.
D
Line b is perpendicular to line c.
10) Triangle MNO has coordinates M(0, 2), N(1, 0), and O(5, 1). What type of triangle is  MNO?
A
equilateral
B
isosceles
C
right
D
scalene
11) A gardener wants to enclose a circular garden with a square fence, as shown. If the circumference
of the circular garden is about 48 feet, which of the following is the approximate length of fencing
needed?
A
31 ft
B
61 ft
C
122 ft
D
244 ft
12) The exterior angle of a base angle in an isosceles triangle is 100°. What is the measure of the
vertex angle?
A
3
20°
B
40°
C
60°
D
80°
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
13) Point J (p, q) is a vertex of quadrilateral JKLM. What are the coordinates of J′ after JKLM is
rotated 180° about the origin?
A
(-p, -q)
B
(-p, q)
C
(p, -q)
D
(q, -p)
14)  GHI will be dilated by a scale factor of 3, resulting in GH I  . What rule describes this
transformation?
1 1 
A (x′, y′) =  x, y 
B (x′, y′) = (3x, 3y)
3 3 
C
(x′, y′) = (x + 3, y + 3)
D
(x′, y′) = (x − 3, y − 3)
15)  P΄Q΄R΄ is the image produced after reflecting  PQR across the y-axis. If vertex P has
coordinates (s, t), what are the coordinates of P  ?
A
(t, s)
B
(s, −t)
C
(−s, −t)
D
(−s, t)
16) What is the rule for the transformation formed by a translation 2 units to the left and 3 units up
followed by a 90° counterclockwise rotation?
A
(x′′, y′′) = (-3y, -2x)
B
(x′′, y′′) = (x − 2, y + 3)
C
(x′′, y′′) = [−(y + 3), x − 2]
D
(x′′, y′′) = [−(y - 3), x + 3]
17) The point G(2, -7) is transformed according to the rule (x′, y′) = (x + 2, y − 3). The image G′ of the
transformation is then reflected over the line y = x, resulting in point G′′. What are the coordinates of
G′′?
A
(4, 10)
B
(4, -10)
C
(-10, 4)
D
(-4, 10)
18)  G′H′I′ is the image of  GHI after a transformation. Which choice describes the transformation
shown?
4
A
reflection over x-axis
B
reflection over y-axis
C
(x′, y′) = (x − 8 , y)
D
(x′, y′) = (x, y− 8)
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
19)  XYZ is dilated by a factor of ½. What is the ratio of the area of  XYZ to the area of its image,
 X′Y′Z′?
A
4:1
B
2:1
C
1:2
D
1:4
20) In the coordinate plane, right triangle XYZ is reflected over the line y = x. What are the
coordinates of the vertex of the right angle in X Y Z  ?
A
(3, 1)
B
(3, 0)
C
(1, -3)
D
(1, -2)
 2 3 3 
1
21)  GHJ with vertex matrix 
is dilated by a factor of . In the image  G′H′J′, what

3
 4 6  2
are the coordinates of the vertex that lies in the second quadrant?
A
 7 13 
 , 
 3 3
B
 2
1, 
 3
C
 2 4
 , 
 3 3
D
(1, 2)
22) The vertices of quadrilateral GHIJ are G(-1, -1), H(3, -2), I(2, 4), and J(-2, 3). G′H′I′J′ is the
image produced by translating quadrilateral GHIJ 6 units to the left. What are the coordinates of
G′H′I′J′?
23)  M′N′O′ is the image of  MNO produced by a translation 3 units left and 1 unit up. The vertex
 1 2 4 
matrix for M N O is 
 . What are the coordinates for  MNO?
 1 6  3
5
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
24) A cylinder with a height of 4 centimeters has a base whose area is 3 square centimeters. If the
cylinder is being filled with water at a rate of 2 cubic centimeters per second, how long will it take to
fill the cylinder?
A
6s
B
8s
C
12 s
D
24 s
25) In the figure, lines a and b are parallel and transversals c and d intersect at point X. Which of the
following is a valid statement?
A
PQX  XSR by the Corresponding Angles Postulate
B
PQX  SRX by the AA Similarity Postulate
C
PQX  RSX by the ASA Similarity Postulate
D
PXQ  RXS by the Alternate Interior Angles Theorem
26) Are the two triangles (not drawn to scale) similar? If so, explain why they are.
30
16
17
62°
28°
28°
34
62°
8
15
27) Determine whether the figures are similar.
4.2
11
120°
7
7
7.7
7.7
120°
11
4.2
6
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
28) ABC and XYZ are similar with A  X and B  Y . If AB, BC, and AC are 5 inches, 12
inches, and 13 inches, respectively, and XY is 9 inches, find XZ. (Answer to the nearest tenth.)
A
23.4 in.
B
21.6 in.
C
6.7 in.
D
7.2 in.
29) Given that ABC ~ DEF solve for x and y.
A
x = 8.2, y = 7.5
B
x = 7.2, y = 65
A
D
9
y
x
6
C
D
x = 8.2, y = 6.5
B
5
C
E
4
F
x = 7.2, y = 7.5
30) What value of x will make the two triangles similar?
x
28
34
40
51
42
31) The volume of the right cone below is _____.
32) The inside of an ice cream cone is filled with ice cream and has radius 4 cm and height 12 cm.
Assuming that a half-scoop of ice cream is in the shape of a hemisphere, and that it fits perfectly on top
of the cone (same radius), find the total volume of ice cream. Use 3.14 for  and round your answer to
the nearest tenth.
7
A
736.9 cm3
B
334.9 cm3
C
385.2 cm3
D
468.9 cm3
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
33) The top of the cylindrical container below has the shape of a hemisphere. The total volume of the
container is _____.
A
36 in.3
B
36 in.3
C
18 in.3
D
27 in.3
34) Find the measure of an angle that is twice as large as its supplement.
A) 30°
B) 60°
C) 90°
D) 120°
35) Which of the following is the reason that 3  5 ?
A) If two parallel lines are cut by a transversal, then corresponding angles are congruent.
B) If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
C) If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
D) If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
36) Find the values of x, y, and z.
A) x = 10, y = 20, z = 120
B) x = 10, y = 40, z = 160
C) x = 20, y = 20, z = 120
D) x = 20, y = 40, z = 140
8
8th Grade EOG Geometry Review 2014-2015
Name_______________________Date________
Use the figure at the right to answer Questions 37–39.
37) If m2  145° and 4  6 , find m5
A) 35°
B) 70°
C) 72.5°
D) 107.5°
38) If m1  5x  5 , and m7  4x  4 , find m1.
A) 9°
B) 40°
C) 96°
D) 140°
39) If m3  6x  3, and m10  10x  15 , find m8 .
A) 12°
B) 75°
C) 105°
D) 168°
Use this diagram for #40-42.
40) What kind of angles are 2 and 6 ?
A) Same – side interior angles
1
2
3 4
B) Alternate exterior angle
m
C) Alternate interior angles
5 6
7 8
D) Corresponding angles
41) If the m4  3x  32 , and m5  4x 13 , find x so that m || n.
A) 37
B) 19.3
C) 23
D) 45
C) 108
D) 36
42) If m || n, and m3 = 72, find m5 .
A) 18
9
B) 72
n