PSD Geometry Final Name:_________KEY__________ID:_________ Common Geometry Assessment
KEY
Formulas
P = 4s
A = s2
P = 2b + 2h
SA = LA + 2 B
V = Bh
SA = 2πrh + 2πr 2
A = bh
V = πr 2 h
1
bh
2
1
A = (b1 + b2 )h
2
1
A = ap
2
1
A = d1 d 2
2
V =
A=
1
Bh
3
SA = 4πr 2
4
V = πr 3
3
opp
adj
opp
sin A =
hyp
adj
cos A =
hyp
C = πd = 2πr
tan A =
A = πr 2
d = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2
⎛ x + x 2 y1 + y 2 ⎞
,
M =⎜ 1
⎟
2 ⎠
⎝ 2
PSD Geometry Final Name:_________KEY__________ID:_________ Multiple Choice: Identify the choice that best completes the statement or answers the question.
Please write your choice on the line provided to the right of each question.
1. Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
a. Hypothesis: The two lines are perpendicular.
Conclusion: To lines intersect at right angles.
b. Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.
c. Hypothesis: The two lines are not perpendicular.
Conclusion: Two lines intersect at right angles.
B
d. Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
2. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a.
b.
c.
d.
If a point is in the first quadrant, then its coordinates are positive.
If a point is not in the first quadrant, then the coordinates are not positive.
If the coordinates of a point are positive, then the point is in the first quadrant.
If the coordinates of a point are not positive, then the point is not in the first quadrant.
C
3. Find the value of x.
C
a. -15
b. 94
c. 15
d. 86
4. Find the values of x and y.
D
a. x = 135, y = 45
b. x = 45, y = 135
c. x = 9, y = 35
d. x = 35, y = 9
PSD Geometry Final Name:_________KEY__________ID:_________ 5. From the information in the diagram, can you prove ΔFDG ≅ ΔFDB?
A
a. Yes, by ASA
b. Yes, by AAA
c. Yes, by SAS
d. No
6. Name the theorem or postulate that lets you immediately conclude ΔABD ≅ ΔCBD.
A
a. SAS
b. ASA
c. AAS
d. none of these
7. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale.
B
a. 36
b. 10
c. 39
d. 20
8. Find the length of AB , given that DB is a median of the triangle and AC = 26.
A
a. 13
b. 26
c. 52
d. not enough information
PSD Geometry Final Name:_________KEY__________ID:_________ 9. Given: AB is the perpendicular bisector of IK . Name two lengths that are equal.
D
a. AB = IK
b. IJ = AJ
c. JK = AJ
d. IJ = JK
10. Write a similarity statement for the triangles.
C
a. ΔCDE ~ ΔFHG
b. ΔCED ~ ΔFGH
c. ΔCDE ~ ΔFGH
d. ΔEDC ~ ΔFGH
11. The two rectangles are similar. Which is a correct proportion for corresponding sides?
B
12 x
a.
=
8 4
12 x
b.
=
4 8
12
x
c.
=
4 20
4 x
d.
=
12 8
12. The pentagons are similar. Find x. The figure is not drawn to scale.
A
a. x = 27
b. x = 28
c. x = 9
d. x = 16
PSD Geometry Final Name:_________KEY__________ID:_________ 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.
Find the height of the flagpole to the nearest tenth of a foot.
A
a. 20 ft
b. 38.4 ft
c. 55 ft
d. 25 ft
14. Find the length, x, of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
B
a. 37
b.
210
c. 210
d.
37
15. Given: PQ || BC. Find the length of AQ . The diagram is not drawn to scale.
C
a. 8
b. 7
16. Which statement is true?
a. All quadrilaterals are rectangles.
b. All rectangles are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
c. 4
d. 6
C
PSD Geometry Final Name:_________KEY__________ID:_________ 17. Find the value of x, y, and z in the parallelogram. The diagram is not to scale.
D
a. x = 49, y = 29, z = 102
b. x = 29, y = 49, z = 131
c. x = 49, y = 49, z = 131
d. x = 29, y = 49, z = 102
18. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.
C
a. x = 10, y = 38
b. x = 10, y = 21
c. x = 10, y = 7
d. x = 7, y = 10
19. Find m∠1, m∠2, and m∠3 in the kite. The diagram is not to scale.
B
a. m∠1 = 51, m∠2 = 90, m∠3 = 51
b. m∠1 = 39, m∠2 = 90, m∠3 = 51
c. m∠1 = 39, m∠2 = 90, m∠3 = 39
d. m∠1 = 51, m∠2 = 90, m∠3 = 39
20. For A(1, -1), B(-1, 3), and C(4, -1), find the location of a fourth point, D, so that a parallelogram
is formed using A, B, C, and D in any order as vertices.
a. D(2, 3)
b. D(3, 2)
c. D(3, 3)
d. D(-1, 4)
A
PSD Geometry Final Name:_________KEY__________ID:_________ 21. Find the lengths of the missing sides in the triangle. Write your answers in simplified radical
form.
A
a. x = 9, y = 9 2
c. x = 4.5, y = 4.5 2
b. x = 4.5 2 , y = 4.5
d. x = 9 2 , y = 9
22. Find the values of x and y. Write your answers in simplified radical form.
D
a. x = 17, y = 34 3
c. x = 34 3 , y = 17
b. x = 34, y = 17 3
d. x = 17 3 , y = 34
23. Find the value of x. Round your answer to the nearest tenth.
C
a. 3.3
b. 3.1
c. 24.7
d. 8.5
24. Find the value of x. Round your answer to the nearest tenth.
D
a. 12
b. 8.5
c. 12.4
d. 8.1
PSD Geometry Final Name:_________KEY__________ID:_________ 25. Find the value of x. Round your answer to the nearest tenth.
C
a. 62
b. 25.5
c. 27.8
d. 25
26. To approach the runway, a small plane must begin a 9° descent starting from a height of 1125
feet above the ground. To the nearest tenth of a foot, how many feet from the runway is the
airplane at the start of this approach?
B
a. 7130.0 ft
b. 7191.5 ft
c. 176.0 ft
d. 178.2 ft
27. Find the area of the circle in terms of π.
C
a. 12π in.2
b. 144π in.2
c. 36π in.2
d. 24π in.2
28. If the perimeter of a square is 72 inches, what is its area?
a. 72 in
2
b. 324 in
2
c. 80 in
2
B
d. 5,184 in
2
PSD Geometry Final Name:_________KEY__________ID:_________ 29. Find the area. The figure is not drawn to scale.
A
a. 144.5 cm2
b. 127 cm2
c. 172 cm2
d. 50 cm2
30. Find the area.
D
a. 77.2 in2
b. 80 in2
c. 75 in2
d. 70 in2
31. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.
a. 385 cm
b. 455 cm
c. 14,700 cm
d. 12 cm
32. A kite has diagonals 9.2 feet and 8 feet. What is the area of the kite?
a. 36.8 ft
2
2
b. 8.6 ft
c. 73.6 ft
2
d. 34.4 ft
D
A
2
33. Find the area of a regular hexagon with side 8 yards. Give the answer to the nearest tenth.
D
a. 332.6 yd2
b. 12 yd2
c. 41.6 yd2
d. 166.3 yd2
PSD Geometry Final Name:_________KEY__________ID:_________ 34. Find the surface area of the cylinder in terms of π.
B
a. 688π in2
b. 304π in2
c. 176π in2
d. 208π in2
35. Find the surface area of the cone in terms of π.
A
a. 54π cm2
b. 99π cm2
c. 51π cm2
d. 49.5π cm2
36. Find the volume of the composite space figure to the nearest whole number.
A
a. 447 mm3
b. 595 mm3
c. 207 mm3
d. 347 mm3
37. Find the volume of the square pyramid shown. Round to the nearest tenth.
B
a. 40 cm3
b. 480 cm3
c. 147.3 cm3
d. 720 cm3
PSD Geometry Final Name:_________KEY__________ID:_________ 38. Name the major arc and find its measure.
C
a. arc ADB; 50°
b. arc AB; 50°
c. arc ADB; 310°
d. arc AB; 310°
39. Find the length of arc XY. Leave your answer in terms of π.
C
a. 24π m
b. 12π m
c. 4π m
d. 720π m
40. Find the area of the figure to the nearest tenth.
A
a. 74.2 in2
b. 8.2 in2
c. 148.4 in2
d. 254.5 in2
PSD Geometry Final Name:_________KEY__________ID:_________ Fill in the Blank: Fill in the appropriate reason for the following questions. You can choose from the
following list of possible reasons:
Given
Substitution
Segment Addition Postulate
Angle Addition Postulate
Reflexive Property
Symmetric Property
Transitive Property
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Same-Side Interior Angles Theorem
Triangle Angle-Sum Theorem
Polygon Angle-Sum Theorem
Side-Side-Side (SSS) Postulate
Side-Angle-Side (SAS) Postulate
Angle-Side-Angle (ASA) Postulate
Angle-Angle-Side (AAS) Postulate
Corresponding Parts of Congruent Triangles are
Congruent (CPCTC)
Isosceles Triangle Theorem
Hypotenuse-Leg (HL) Theorem
Angle-Angle (AA~) Similarity Postulate
Side-Angle-Side (SAS~) Similarity Postulate
Side-Side-Side (SSS~) Similarity Postulate
Simplify
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distribution Property
41. Given: AC = 32. Prove: x = 3.
Statements:
Reasons:
a. AB + BC = AC
a. Segment Addition Postulate
b. 2 x + 6 x + 8 = 32
b. Substitution
c. 8 x + 8 = 32
c. Simplify
d. 8 x = 24
d. Subtraction Property of Equality
e. x = 3
e. Division Property of Equality
42. Given: RS ≅ UT and RT ≅ US . Prove: ΔRST ≅ ΔUTS .
Statements:
Reasons:
a. RS ≅ UT and RT ≅ US
a. Given
b. ST ≅ TS
b. Reflexive Property
c. ΔRST ≅ ΔUTS
c. SSS
PSD Geometry Final Name:_________KEY__________ID:_________ 43. Given: ∠Q ≅ ∠T and QR ≅ TR . Prove: PR ≅ SR .
Statements:
Reasons:
a. ∠Q ≅ ∠T and QR ≅ TR
a. Given
b. ∠PRQ ≅ ∠SRT
b. Vertical Angles Theorem
c. ΔPRQ ≅ ΔSRT
c. ASA
d. PR ≅ SR
d. CPCTC
44. Given: a || b. Prove: ∠1 ≅ ∠3 .
Statements:
Reasons:
a. a || b
a. Given
b. ∠1 ≅ ∠2
b. Corresponding Angles Postulate
c. ∠2 ≅ ∠3
c. Vertical Angles Theorem
d. ∠1 ≅ ∠3
d. Substitution or Transitive Property
PSD Geometry Final Name:_________KEY__________ID:_________ 45. In each figure, a pre-image and image are shown. On the line below the figure, describe the
transformation as a translation, a reflection, a rotation, or a dilation.
Reflection
Rotation
Translation
Dilation