Practice%20Test%20Unit%203%20Geometry

1
Practice TestUnit 3Geometry
2
Which of the following points is the greatest
distance from the y-axis?
1
?
A
A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1)
?
B
?
C
?
D
?
E
3
Points P, Q, R, and S lie on a line in that
order. If QR RS, PQ 10, and PS 38, what
does QR equal?
2
38 10 28
10
?
?
?
?
P
Q
R
S
38
QR 28 2
14
4
Find the midpoint between the points (3,6) and
(7,13).
3
5
In the figure below, is a straight
line. What is the value of x?
4
x x 44 180
Straight Line 180?
2x 44 180
44
44
2x 136
x 68
6
Find the area of ?ABC.
5
h
8
b
Side
7 (1) 7 1 8
Note The y-coordinates are the same.
Subtract x-coordinates.
7
Find the area of ?ABC.
5
?
5
h
?
8
b
20
8
Find the length of the line segment AB.
6
Find the length by finding the distance between
the points.
A(3,4)
?
?
B(2,1)
9
Find the length of the line segment AB.
6
Find the length by finding the distance between
the points.
A(3,4)
?
?
B(2,1)
d 5.83
10
Solve for x.
7
Congruent Angles ?4 ?8
m n
m
(x80)?
x 80 5x
n
x
x
(5x)?
80 4x
20 x
1
2
m n
m
?1 ?3 ?5 ?7
4
3
6
5
n
?2 ?4 ?6 ?8
7
8
11
Find the value of x.
8
5y
9x 8
80?
9x 8 80
Vertical Angles
8
8
9x 72
x 8
12
9
If ?PRQ is an isosceles triangle with PQ PR,
find the measure of ?QPX.
?PRQ Isosceles Triangle
The base angles are equal.
?QPX Exterior Angle
60?
?
13
In the figure, if x 2z and y 70, what is the
value of z?
10
70
2z
2z 70 z
Exterior Angles Rule
z
z
z 70
14
11
If the ratio of the angles of a triangle is
234, what is the degree measure of the largest
angle?
Largest Angle 4x
4(20)
80?
15
In the isosceles right triangle ABC, leg
equals 6. What is the length of ?
12
3x 6
x 2
6
5x
5(2)
10
16
13
17
In ?ABC, the measure of ?A is 80 and the
measure of ?B is 50. If the length of AB is 2x
12 and the length of AC is x 3, what is the
length of AB?
14
A
?C 180 80 50
50
80
AB AC
2x 12 x 3
x
x
x 12 3
50
50
x 9
B
C
AB 2(9)12
18 12
6
18
In the right ?ABC, the length of leg is
and D is the midpoint of . Find the
length of .
15
x
3
30
?C 180 ?A ?B
180 60 90
30
19
16
Find the length of JK.
L
34.6 mm
18?
K
J
1 ? x .9511 ? 34.6
x
x 32.91
cos 18? .9511
20
17
Two angles of a hexagon measure 140 each. The
other four angles are equal in measure. What is
the measure of each of the other four equal
angles, in degrees?
Step 1 Find the sum of interior
angles in a hexagon.
x?
x?
? Number of sides
6
140?
140?
? Number of sides 2
6 2 4
x?
x?
? Multiply 4 by 180?
4(180?)
720?
21
Two angles of a hexagon measure 140 each. The
other four angles are equal in measure. What is
the measure of each of the other four equal
angles, in degrees?
17
Step 1 Find the sum of interior
angles in a hexagon.
x?
x?
720?
Step 2 Set up equation by letting sum of
angles equal 720.
140?
140?
x x x x 140 140 720
4x 280 720
x?
x?
280
280
4x 440
Measure of each the four equal angles is 110?
x 110
22
18
A regular octagon is shown. What is the
measure, in degrees, of ?X?
Step 1 Find sum of the interior angles in
the regular octagon.
? Number of sides 8
X
? Number of sides 2
8 2 6
? Multiply 6 by 180?
6(180?)
1080?
Step 2 Find value of each interior angle, ?X.
Divide sum by number of sides, 8.
1080? ? 8
135?
23
In the figure, right triangle ?ABC is contained
within right triangle ?AED. What is the ratio of
the area of ?AED to the area of ?ABC?
19
?ABC is Isosceles
45?
?AED Big Triangle
45?
?A 45?
?D 90?
?E 45?
?AED is Isosceles
45?
8
24
In the figure, right triangle ?ABC is contained
within right triangle ?AED. What is the ratio of
the area of ?AED to the area of ?ABC?
19
Area of ?ABC Small Triangle
45?
18
45?
Area of ?AED Big Triangle
32
45?
8
25
The figure above shows a square region divided
into four rectangular regions, three of which
have areas 5x, 5x, and x2, respectively. If the
area of MNOP is 64, what is the area of square
QROS?
20
x
5
Area of square QROS
5
5
Length ? Width
5 ? 5
25
x
x
x
5
26
All the dimensions of a certain rectangular solid
are integers greater than 1. If the volume is
126 cubic inches and the height is 6 inches, what
is the perimeter of the base?
21
V Volume
Perimeter of Base
V l?w?h
2l 2w
126 l ? w ? 6
2(7) 2(3)
14 6
6
20
21 l ? w
(Base)
Base
l 3 or 7
w 3 or 7
27
22
In trapezoid ABCD, AB CD. What is the value of
x?
Method 1
Isosceles Trapezoid
?A and ?B supplementary
75 x 180
75
75
x 105
28
22
In trapezoid ABCD, AB CD. What is the value of
x?
Method 2
Sum of all angles 360
x x 75 75 360
2x 150 360
150
150
2x 210
x 105
29
23
Cube A has an edge of 2. Each edge of cube A is
increased by 50, creating a second cube B. The
surface area of cube B is how much greater than
the surface area of cube A?
50 of 2
.50 ? 2
1
2 1 3
50 increase
30
23
Cube A has an edge of 2. Each edge of cube A is
increased by 50, creating a second cube B. The
surface area of cube B is how much greater than
the surface area of cube A?
SA Surface Area
SA 6s2
SA 6s2
6?22
6?32
6?4
6?9
24
54
54 24
31
24
In the figure, VW WX VX XY YZ XZ. If
VZ 12, what is the perimeter of the triangle
VWX?
VZ 12
VX 6
VW 6
WX 6
Perimeter ?VWX 6 6 6 18
32
25
If the diameter of circle is 8, what is the ratio
between the circles area and its circumference?
d 2r
Step 1 Find the radius, given diameter is 8.
d 8
r 4
Step 2 Find circumference of circle.
Step 3 Find area of circle.
C 2pr
A pr2
2p?4
8p
p?16
16p
p?42
33
25
If the diameter of circle is 8, what is the ratio
between the circles area and its circumference?
Step 2 Find circumference of circle.
Step 3 Find area of circle.
C 2pr
A pr2
2p?4
8p
p?16
16p
p?42
Step 4 Find ratio.
2
21
34
26
Find the circumference of a circle with area p.
C 2pr
C Circumference
A Area
Find the radius
A pr2
C Circumference
A p
p pr2
C 2pr
C 2p ? 1
C 2p
1 r2
1 r
35
If a circle with an area of 4? is inscribed in a
square , what is the perimeter of the square?
27
A Area
4
P Perimeter
A 4p
P 4s
A pr2
P 4(4)
d 4
?
4p pr2
r 2
P 16
(Find radius)
4 r2
2 r
36
In the figure, the circle inscribed inside the
square has a radius of 3. What is the area of
the shaded region?
28
6
Circle Area
Square Area
A pr2
A s2
A p32
A 62
d 6
?
A 36
3
A p9
A 9p
Area of shaded region
Square Area Circle Area
36 9p
37
The circle has a diameter of 12. What is the
length of ?
29
Length of major arc
6
C 2pr
9p
C 2p ? 6
12p
38
If the circumference of the circle is 8?, what is
the area of the shaded region?
30
Area of circle
Circumference
C 2pr
A pr2
C 8p
A p ? 42
8p 2pr
A p ? 16
4 r
A 16p
Central Angle 90
Area of sector
4p
39
?ABC 48. Find the measure of the major arc
.
31
Major Arc in red
48?
48?
Major Arc
360? 48?
312?
40
If , find the measure of
?CDE.
32
60?
41
In the figure, if the slope of line m is
, what is the value of y ?
33
Use the slope formula.
4(y 8) 8 ? 3
4y 32 24
32
32
4y 8
42
34
If a straight line intersects the x-axis at 5 and
the y-axis at 3, what is the slope of the line?
5
?
3
?
43
35
Which line is parallel to the line 2y 3x 4 ?
Note Parallel lines have the same slope.
Step 1 Find the slope of 2y 3x 4
by rewriting in slope-intercept
form, y mx b

• 6y 3x 4
• 2y x 2
• C. 4y 6x 1
• y 3x 4
• E. 2y 2x 1

2y 3x 4
44
Which line is parallel to the line 2y 3x 4 ?
35
Note Parallel lines have the same slope.
Step 2 Find the slope of each answer
by rewriting in slope-intercept
form, y mx b
2y 3x 4

6y 3x 4
NO
Slopes not equal
45
Which line is parallel to the line 2y 3x 4 ?
35
Note Parallel lines have the same slope.
Step 2 Find the slope of each answer
by rewriting in slope-intercept
form, y mx b
2y 3x 4
B.
2y x 2
NO
Slopes not equal
46
Which line is parallel to the line 2y 3x 4 ?
35
Note Parallel lines have the same slope.
Step 2 Find the slope of each answer
by rewriting in slope-intercept
form, y mx b
2y 3x 4
C.
4y 6x 1
Slopes are equal
47
36
A, B, C, and D are points in the coordinate
system. Segments AB, BC, CD, and DA form a
rectangle. The slope of line AB is . What
is the slope of line BC.
48
A, B, C, and D are points in the coordinate
system. Segments AB, BC, CD, and DA form a
rectangle. The slope of line AB is . What
is the slope of line BC.
36
Perpendicular Lines have slopes that are negative
reciprocals
49
Which line segment in the figure has a slope of
?
37
?
?
?
They rise as you trace them from left to right.
Thus, they can not be the answer.
?
50
Which line segment in the figure has a slope of
?
37
5
?
4
?
51
Which line segment in the figure has a slope of
?
37
3
?
3
?
52
Which line segment in the figure has a slope of
?
37
3
?
2
?
53
Find the equation of the given graph.
38
?
Start at origin.
Shift left 2 units.
Shift down 1 unit.
54
Find the equation of the given graph.
39
?
Start at origin.
Shift right 3 units.
Reflect on x-axis.
55
40
A parabola with in equation of the form y ax2
bx c has the point (3,1) as its vertex. If
(1,3) also lies on the parabola, which of the
following is another point on this parabola?
Mirror Image Points
x 1
x 5
x 3
?
?
(1,3)
(?,3)
(5,3)
x-coordinates are same distance from axis of
symmetry
?
(3,1)
56
Which parabola intersects the x-axis in two
distinct points?
41
A. y (x 5)2
B. y (x 5)2
?
?
Touches x-axis at 1 point
Touches x-axis at 1 point
57
Which parabola intersects the x-axis in two
distinct points?
41
E. y (x 4)2
C. y x2 25
D. y x2 25
?
?
?
Touches x-axis at 1 point
Touches x-axis at 2 points
Touches x-axis at 0 points
58
42
Which of the following are solutions to the
equation x2 2x 8 ?
Substitute each answer for x into equation x2
2x 8. Then, determine if both sides are equal.

• 8 and 1
• 1 and 8
• 4 and 2
• 4 and 2
• E. 4 and 2

NO
Test x 1
Test x 8
x2 2x 8
x2 2x 8
(1)2 2(1) 8
(8)2 2(8) 8
1 2 8
64 (16) 8
3 ? 8
48 ? 8
59
Which of the following are solutions to the
equation x2 2x 8 ?
42
Substitute each answer for x into equation x2
2x 8. Then, determine if both sides are equal.

• 8 and 1
• 1 and 8
• 4 and 2
• 4 and 2
• E. 4 and 2

NO
Test x 8
If one answer does not work, then the whole
answer is wrong.
x2 2x 8
NO
(8)2 2(8) 8
64 16 8
80 ? 8
60
Which of the following are solutions to the
equation x2 2x 8 ?
42
Substitute each answer for x into equation x2
2x 8. Then, determine if both sides are equal.

• 8 and 1
• 1 and 8
• 4 and 2
• 4 and 2
• E. 4 and 2

NO
Test x 2
If one answer does not work, then the whole
answer is wrong.
NO
x2 2x 8
(2)2 2(2) 8
NO
4 (4) 8
NO
0 ? 8
61
Which of the following are solutions to the
equation x2 2x 8 ?
42
Substitute each answer for x into equation x2
2x 8. Then, determine if both sides are equal.

• 8 and 1
• 1 and 8
• 4 and 2
• 4 and 2
• E. 4 and 2

NO
Test x 2
Test x 4
x2 2x 8
x2 2x 8
NO
(2)2 2(2) 8
(4)2 2(4) 8
NO
4 4 8
16 (8) 8
NO
8 8
8 8