1. Practice Test Unit 3 Geometry
Tuesday, September 18, 2018Tuesday, September 18, 2018

2.      A B C D E A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1)
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
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).

5. x + x + 44 = 180 Straight Line 180 2x + 44 = 180 –44 –44 2x = 136
In the figure below, is a straight line.
What is the value of x?
x + x + 44 = 180
Straight
Line
180
2x + 44 = 180
–44
–44
2x = 136
x = 68

6. h b 7 – (–1) = 7 + 1 = 8 Find the area of ABC. 5 8 Side
Note: The y-coordinates are the same.
7 – (–1)
= = 8
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. d ≈ 5.83   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. 7 Solve for x. Congruent Angles 4 = 8 (x+80) x + 80 = 5x –x –x
m || n m
(x+80)
x + 80 = 5x n –x –x
(5x)
80 = 4x
20 = x
m || n 1 2 m 4 3
1 = 3 = 5 = 7 5 6 n
2 = 4 = 6 = 8 8 7

11. Find the value of x. 5y 9x + 8 80 9x + 8 = 80 Vertical Angles – 8 – 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. 2z = 70 + z – z – z z = 70 70 2z 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 2:3:4, what is the degree measure of the largest angle?
Largest Angle 4x
4(20)
= 80

15. 12
In the isosceles right triangle ABC, leg equals 6. What is the length of ?
3x = 6
x = 2 6
= 5x
= 5(2)
= 10

16. 13

17. A C = 180° – 80° – 50° = 50° 80° AB = AC 2x – 12 = x – 3 –x –x
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 15
In the right ABC, the length of leg is
and D is the midpoint of Find the length of 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 =  34.6 x
x =
cos 18 = .9511

20. x x 140 140 x x Step 1: Find the sum of interior17
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. Measure of each the four equal angles is 110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
720
Step 2: Set up equation by
letting sum of angles equal 720.
140
140
x + x + x + x = 720
4x = 720 x x
– 280
– 280
Measure of each the four equal angles is 110
4x = 440
x = 110

22. A regular octagon is shown. What is the measure, in degrees, of X?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. ∆ABC is Isosceles ∆AED Big Triangle A = 45 D = 90 E = 4519
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?
∆ABC is Isosceles
45
∆AED Big Triangle
45
A = 45
D = 90
E = 45
∆AED is Isosceles
45 8

24. 19
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?
Area of ∆ABC Small Triangle
45
= 18
45
Area of ∆AED Big Triangle
= 32
45 8

25. x 5 5 5 x x x 5 Area of square QROS = 5  5 = 25 20
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? x 5
Area of square QROS
Length  Width 5 5
= 5  5
= 25 x x x 5

26. V = Volume V = lwh 2l + 2w 126 = l  w  6 = 2(7) + 2(3) = 14 + 621
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?
V = Volume
Perimeter of Base
V = lwh
2l + 2w l w h
126 = l  w  6
= 2(7) + 2(3) = 6
21 = l  w
= 20
(Base)
Base
l = 3 or 7
w = 3 or 7

27. A and B supplementary 75° + x = 180°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 = 360
2x = 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? 2
Cube A
Cube B 3
50% of 2
= .50  2
= 1
50% increase =
2 + 1 = 3

30. = = 622 = 632 = 64 = 69 = 24 = 54 – 54 – 24 30 SA = 6s2 SA = 6s223
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 2
Cube A
Cube B 3
SA = 6s2
SA = 6s2
= 622
= 632
= 64
= 69
= 24
= 54
SA Cube B
SA Cube A – – = 30

31. VZ = 12 VX = 6 VW = 6 WX = 6 Perimeter VWX = 6 + 6 + 6 = 1824
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 = = 18

32. d: diameter r: radius d = 2r d = 8 r = 4 C = 2πr A = πr2 = 2π4 = 8π25
If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference?
d: diameter
r: radius
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 = 2πr
A = πr2
= 2π4
= 8π
= π42
= π16
= 16π

33. C = 2πr A = πr2 = 2π4 = 8π = π42 = π16 = 16π = 2 = 2:1 25
If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference?
Step 2
Find circumference of circle.
Step 3
Find area of circle.
C = 2πr
A = πr2
= 2π4
= 8π
= π42
= π16
= 16π
Step 4: Find ratio.
= 2
= 2:1

34. C: Circumference C = 2πr A: Area Find the radius A = πr2 A = π26
Find the circumference of a circle with area π.
C: Circumference
C = 2πr
A: Area
Find the radius
A = πr2
A = π
C: Circumference
π = πr2
C = 2πr
C = 2π  1
C = 2π
1 = r2
1 = r

35. 27
If a circle with an area of 4 is inscribed in a square , what is the perimeter of the square? 4
A: Area
P: Perimeter
A = 4π
P = 4s
A = πr2
d = 4
P = 4(4) 
r = 2
4π = πr2
P = 16
(Find radius)
4 = r2
2 = r

36. = Square Area – Circle Area
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 = πr2
A = s2
d = 6
A = π·32
A = 62  3
A = π·9
A = 36
A = 9π
Area of shaded region
= Square Area – Circle Area
= 36 – 9π

37. 29
The circle has a diameter of 12. What is the length of ?
Length of major arc 6
C = 2πr
= 9π
C = 2π  6
= 12π

38. 30
If the circumference of the circle is 8, what is the area of the shaded region?
Circumference
Area of circle
C = 2πr
A = πr2
C = 8π
A = π  42
8π = 2πr
A = π  16
4 = r
Central Angle = 90°
A = 16π
Area of sector
= 4π

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
y = 2

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. 2y = 3x + 4 Which line is parallel to the line 2y = 3x + 4 ?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. 35
Which line is parallel to the line 2y = 3x + 4 ?
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 NO
6y = 3x – 4
Slopes
not equal

45. 35
Which line is parallel to the line 2y = 3x + 4 ?
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. NO
2y = x + 2
Slopes
not equal

46. 35
Which line is parallel to the line 2y = 3x + 4 ?
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. form a rectangle. The slope of line AB is . 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. A B C D A B C D

48. form a rectangle. The slope of line AB is . 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. A B C D
Perpendicular Lines
have slopes that are
negative reciprocals

49.     37 Which line segment in the figure has a slope of ? Use
to find the slope for
each line segment. 
Segments and
have positive slopes.  
They rise as you trace them from left to right.
Thus, they can not be the answer. 

50.   –5 4 37 Which line segment in the figure has a slope of ? Use
to find the slope for
each line segment. –5  4 

51.   –3 3 37 Which line segment in the figure has a slope of ? Use
to find the slope for
each line segment. –3  3 

52.   –3 2 37 Which line segment in the figure has a slope of ? Use
to find the slope for
each line segment. –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 = 3
x = 5
(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
C. y = x2 – 25
D. y = x2 + 25
E. y = (x – 4)2   
Touches x-axis
at 1 point
Touches x-axis
at 2 points
Touches x-axis
at 0 points

58. Which of the following are solutions to the equation x2 + 2x = 8 ?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. If one answer does not work, then the whole answer is wrong.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 = 8
If one answer does not work, then the whole answer is wrong.
x2 + 2x = 8 NO
(8)2 + 2(8) = 8
= 8
80  8

60. If one answer does not work, then the whole answer is wrong.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 = –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
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 = 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