Title: Practice%20Test%20Unit%203%20Geometry
1Practice TestUnit 3Geometry
2Which 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
3Points 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
4Find the midpoint between the points (3,6) and
(7,13).
3
5In 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
6Find the area of ?ABC.
5
h
8
b
Side
7 (1) 7 1 8
Note The y-coordinates are the same.
Subtract x-coordinates.
7Find the area of ?ABC.
5
?
5
h
?
8
b
20
8Find the length of the line segment AB.
6
Find the length by finding the distance between
the points.
A(3,4)
?
?
B(2,1)
9Find 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
10Solve 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
11Find the value of x.
8
5y
9x 8
80?
9x 8 80
Vertical Angles
8
8
9x 72
x 8
129
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?
?
13In 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
1411
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?
15In the isosceles right triangle ABC, leg
equals 6. What is the length of ?
12
3x 6
x 2
6
5x
5(2)
10
1613
17In ?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
18In 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
1916
Find the length of JK.
L
34.6 mm
18?
K
J
1 ? x .9511 ? 34.6
x
x 32.91
cos 18? .9511
2017
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?
21Two 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
2218
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?
23In 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
24In 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
25The 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
26All 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
2722
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
2822
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
2923
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
3023
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
3124
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
3225
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
3325
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
3426
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
35If 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
36In 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
37The circle has a diameter of 12. What is the
length of ?
29
Length of major arc
6
C 2pr
9p
C 2p ? 6
12p
38If 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?
40If , find the measure of
?CDE.
32
60?
41In 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
4234
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
?
4335
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
44Which 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
45Which 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
46Which 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
4736
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.
48A, 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
49Which 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.
?
50Which line segment in the figure has a slope of
?
37
5
?
4
?
51Which line segment in the figure has a slope of
?
37
3
?
3
?
52Which line segment in the figure has a slope of
?
37
3
?
2
?
53Find the equation of the given graph.
38
?
Start at origin.
Shift left 2 units.
Shift down 1 unit.
54Find the equation of the given graph.
39
?
Start at origin.
Shift right 3 units.
Reflect on x-axis.
5540
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)
56Which 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
57Which 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
5842
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
59Which 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
60Which 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
61Which 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