KEY
VERSION A
Common Geometry Assessment
Formulas
Square
P = 4s
A = s2
Cone
Rectangle
P = 2b + 2h
A = bh
Triangle
1
A = bh 2
Trapezoid
A=
1
h(b1 + b2 ) 2
Regular Polygon
A=
1
ap 2
Rhombus or Kite
A=
1
d1d 2 2
SA = LA + B
= π rl + π r 2
1
V = Bh
3
1
V = π r 2h
3
Arc Length
Length =
arc measure
⋅ 2π r 360
Area of Sector
A=
arc measure
⋅π r 2 360
Pythagorean Theorem
a2 + b2 = c2
Special Right Triangles
Parallelogram
A = bh
Circle
C = π d = 2π r
A = πr2
Sphere
SA = 4π r 2
4
V = π r3
3
Prism
SA = LA + 2 B
SA = ph + 2 B V = Bh
Cylinder
SA = 2π rh + 2π r 2
V = π r 2h
Pyramid
SA = LA + B
1
SA = pl + B
2
1
V = Bh
3
Right Triangle Trigonometry
adj
hyp
opp
sin A =
hyp
opp
tan A =
adj
cos A =
Distance
d=
(x 2 − x1 )2 + ( y 2 − y1 )2
Midpoint
⎛ x + x 2 y1 + y 2 ⎞
,
M =⎜ 1
⎟
2 ⎠
⎝ 2
Multiple Choice: Identify the choice that best completes the statement or answers the question.
1. Identify the hypothesis and conclusion of this conditional statement:
If yesterday was Friday, then today is Saturday.
a. Hypothesis: Yesterday was Friday.
Conclusion: Today is not Saturday.
b. Hypothesis: Yesterday was Friday.
Conclusion: Today is Saturday.
c. Hypothesis: Today is Saturday.
Conclusion: Yesterday was Friday.
d. Hypothesis: Today is not Saturday.
Conclusion: Yesterday was Friday.
2. Draw a conclusion from the two given statements.
If two angles are congruent, then they have equal measurements.
∠ P and ∠ Q are congruent.
a.
b.
c.
d.
m∠ P + m∠ Q = 90
∠ P is the complement of ∠ Q.
m∠ P ≠ m∠ Q
m∠ P = m∠ Q
3. Fill in the missing reasons.
Given: ∠Q ≅ ∠T and QR ≅ TR . Prove: PR ≅ SR .
Statements:
Reasons:
1. ∠Q ≅ ∠T and QR ≅ TR
1. Given
2. ∠PRQ ≅ ∠SRT
2. ____________________
3.
ΔPRQ ≅ ΔSRT
4. PR ≅ SR
⎧2.
⎩3.
⎧2.
b. ⎨
⎩3.
a. ⎨
3. ____________________
4. Corresponding Parts of Congruent
Triangles are Congruent
⎧2.
⎩3.
⎧2.
d. ⎨
⎩3.
Vertical Angles Theorem
ASA
Angle Addition Postulate
ASA
c. ⎨
Vertical Angles Theorem
SSS
Angle Addition Postulate
AAS
4. Find the value of x and find the measure of angle ACB.
a. x = -19
c. x = 19
b. x = 72
d. x = 108
m∠ACB = 82
m∠ACB = 13
5. Find the values of x and y.
a. x = 18, y = 42
b. x = 40, y = 42
c.
x = 18, y = 40
d. x = 40, y = 18
m∠ACB = 108
m∠ACB = 108
6. Name the theorem or postulate that lets you immediately conclude ΔABD ≅ ΔCBD.
a. SAS
b. ASA
c.
AAS
d. SSS
7. Q is equidistant from the sides of ∠TSR. Find the value of x.
a. x = 16
b. x = 3
c.
x = 19
d. x = 33
8. Find the length of AB , given that DB is a median of the triangle and AC = 42.
a. 21
b. 42
c.
63
d. 84
9. Given: AB is the perpendicular bisector of
IK . Name two lengths that are equal.
a. AB = IK
b. IJ = AJ
c.
JK = AJ
d. IJ = JK
10. Which of the following is a correct similarity statement for the given triangles?
a. ΔCDE ~ ΔFHG
b. ΔCED ~ ΔFHG
c.
ΔCDE ~ ΔFGH
d. ΔEDC ~ ΔFGH
11. The two rectangles are similar. Which is a correct proportion for corresponding sides?
a.
12 x
=
8 4
c.
12
x
=
4 20
b.
12 4
=
x 8
d.
4 x
=
8 12
12. The pentagons are similar. Find x.
a. x = 9
b. x = 16
c.
x = 27
d. x = 28
13. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from
the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5
feet above the ground and she was 12 feet from the mirror. What is the height of the flagpole? Round your
answer to the nearest tenth of a foot.
a. 20.0 ft
b. 38.4 ft
c.
55.0 ft
d. 25.0 ft
14. Find the length, x, of the altitude drawn to the hypotenuse.
a. x = 22
b. x =
c.
72
x = 22
d. x = 72
15. Given: PQ || BC. Find the length of AP .
a. x = 8
b. x = 7
c.
x=6
d. x = 4
16. Which statement is true?
a. All rectangles are squares.
b. All quadrilaterals are squares.
c. All quadrilaterals are parallelograms.
d. All squares are quadrilaterals.
17. Find the value of x, y, and z in the parallelogram.
a. x = 36, y = 33, z = 111
b. x = 33, y = 36, z = 111
c.
x = 36, y = 33, z = 147
d. x = 33, y = 33, z = 147
18. Find values of x and y for which ABCD must be a parallelogram.
a. x = 6, y = 4
b. x = 4, y = 7
c.
x = 4, y = 6
d. x = 4, y = 23
19. m∠ R = 130 and m∠ S = 80. Find m∠ T.
a. 65
b. 70
c.
35
`
d. 80
20. Given A(1, -1), B(-1, 3), and C(4, -1); find a fourth point, D, so that ABCD is a parallelogram.
a. D(2, 3)
b. D(3, 2)
c.
D(3, 3)
d. D(-1, 4)
21. Find the distance between the points A(1, -1) and B(-1, 3). Round your answer to the nearest tenth.
a. 3.5
b. 2.8
c. 2.0
d. 4.5
22. Find the coordinates of the midpoint of the segment with endpoints B(-1, 3) and C(4, -1).
a. (2.5, 1)
b. (1.5, 1)
c. (2.5, -2)
d. (-1, 3.5)
23. Find the lengths of the missing sides in the triangle. Write your answers in simplified radical form.
a. x = 9, y = 9 2
b. x = 4.5 2 , y = 4.5
c.
x = 9, y = 4.5 2
d. x = 9 2 , y = 9
24. Find the values of x and y. Write your answers in simplified radical form.
a. x = 17, y = 34 3
b. x = 34, y = 17 3
c.
x = 34 3 , y = 17
d. x = 17 3 , y = 34
25. What is the ratio that could be used to find the value of x?
x
9
x
b. tan 20 =
9
a.
cos 70 =
9
x
9
d. sin 20 =
x
c. tan 20 =
26. Find the value of x. Round your answer to the nearest tenth.
a. x = 14.6
b. x = 18.6
c.
x = 18.1
d. x = 14.1
27. Find the value of x. Round your answer to the nearest tenth.
a. x = 42.0
b. x = 64.2
c.
x = 25.8
d. x = 65.0
28. For a small plane to land on the runway safely, the plane must begin a 9° descent (start going down) starting from
a height of 1125 feet above the ground. How many feet from the runway is the airplane when it starts to go
down? Round your answer to the nearest tenth of a foot.
a. 7191.5 ft
b. 7130.0 ft
c.
176.0 ft
d. 178.2 ft
29. Find the area of the circle in terms of π.
a. 36π in.2
b. 324π in.2
c.
18π in.2
d. 81π in.2
30. Find the area of the composite figure.
a. 144.5 cm2
b. 127 cm2
c.
171.5 cm2
d. 50 cm2
31. Find the area of the trapezoid.
a. 50 in2
b. 40 in2
c.
34 in2
d. 28 in2
32. The area of a triangle is 375 cm2 and the height is 15 cm. Find the length of the base.
a. 12.5 cm
b. 25 cm
c. 30 cm
d. 50 cm
33. A kite has diagonal lengths of 3.1 feet and 8 feet. What is the area of the kite?
a. 5.55 ft2
b. 12.4 ft2
c. 22.2 ft2
d. 24.8 ft2
34. Find the area of a regular hexagon with side length 8 yards. Give the answer to the nearest tenth.
a. 332.6 yd2
b. 12.0 yd2
c.
41.6 yd2
d. 166.3 yd2
35. Find the surface area of the cylinder in terms of π.
a. 224π in2
b. 96π in2
c.
112π in2
d. 128π in2
36. Find the surface area of the cone in terms of π.
a. 105π cm2
b. 115.5π cm2
c.
140π cm2
d. 231π cm2
37. Find the volume of the square pyramid shown. Round to the nearest tenth.
a. 328.3 cm3
b. 1404.0 cm3
c.
78.0 cm3
d. 2106.0 cm3
38. Find the volume of the composite space figure to the nearest whole number.
a. 447 mm3
b. 595 mm3
c.
207 mm3
d. 347 mm3
39. Name the major arc of circle C and find its measure.
a. arc ADB; 50°
b. arc AB; 50°
c.
arc ADB; 310°
d. arc AB; 310°
40. Find the length of arc XY. Leave your answer in terms of π.
a. 12π m
b. 2π m
c.
6π m
d. 360π m
41. Find the area of the figure to the nearest tenth.
a. 21.3 in2
b. 8.4 in2
c.
67.0 in2
d. 134.0 in2
42. What type of transformation is represented by the figure?
a. Reflection
b. Translation
c.
Rotation
d. Dilation
43. Find the image of P(-3, 2) after being translated left 4 and reflected across the x-axis.
a. (2, -7)
b. (-7, -2)
c.
(-3, 6)
d. (7, 2)
NOTE: Teachers should use their professional judgement when
scoring the Fill in the Blank if students enter a different but
acceptable answer than the ones given here.
Fill in the Blank: Fill in the missing statement or reason to complete the following proofs. 44. Given: AC = 32. Prove: x = 3.
Statements:
Reasons:
a. AC = 32
Given
a. ___________________
b. AB + BC = AC
Addition Postulate
b. Segment
___________________
c. 2 x + 6 x + 8 = 32
Substitution
c. ___________________
d. 8 x + 8 = 32
Simplify
d. ___________________
e. 8 x = 24
Subtraction Property of Equality
e. ___________________
f. x = 3
Division Property of Equality
f. ___________________
45. Given: a || b. Prove: The Alternate Exterior Angle Theorem (by showing that ∠1 ≅ ∠3 ).
Statements:
Reasons:
a || b
a. ___________________
b.
∠1 ≅ ∠2
Given
a. _____________________
Corresponding Angles Postulate
b. _____________________
Angle 2 congruent to Angle 3
c. ___________________
Vertical Angles Theorem
c. _____________________
d. ∠1 ≅ ∠3
Substitution or Transitive Property
d. _____________________