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Name: ______________________ Class: _________________ Date: _________ ID: A
Geometry EOC Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. In the diagram below, which expression represents x , the degree measure of the exterior angle shown?
a. a + b b. a – b c. a + c d. b + c
____ 2. In the proof below, which triangle congruence property is missing in the last step?
Given: ABCD is a kite
Prove: ABE ≅ CBE
Statement Reason
- ABCD is a kite 1. Given
2. AB ≅ BC ; AD ≅ CD
- Definition of a kite
3. BD ≅ BD
- Reflexive Property
4. ABD ≅ CBD 4. SSS
5. ∠ ABE ≅ ∠ CBE 5. CPCTC
6. BE ≅ BE
- Reflexive Property
7. ABE ≅ CBE 7.?
a. SAS c. AAS
b. SSS d. ASA
____ 3. An exterior angle of a regular polygon has a measure of 18°. How many sides does the polygon have?
a. 10 b. 16 c. 18 d. 20
____ 4. Compare PR and QS.
a. PR = QS
b. PR < QR
c. PR > QS
d. PR < QS
____ 5. In the triangle below, x = 7 yards. What is the value of y?
a. 7 yards c. 14 yards
b. 7 3 yards d. 14 3 yards
____ 8. The side lengths of the smaller hexagon were increased by a factor of 2 to make the larger hexagon. If
the area of the smaller hexagon is 9 3 square units, what is the area of the larger hexagon?
a. 36 3 square units c. 18 6 square units
b. 18 3 square units d. 9 6 square units
____ 9. Which statement is NOT true about the figure?
a. It has 6 vertices.
b. It has 8 edges.
c. It has 5 faces.
d. It is a triangular prism.
____ 10. Triangle LMN has the vertices shown on the coordinate grid.
What is the length of MN?
a. 3 5 units b. 2 13 units c. 58 units d. 65 units
____ 11. Francesco built a box to store his baseball cards. The box is shown below.
Francesco needed more storage and built a similar box that was one-half of each the length, the width,
and the height of the first box. By what factor does the change in dimension between the two boxes
affect the volume?
a. The volume of the smaller box is
of the volume of the larger box.
b. The volume of the smaller box is
of the volume of the larger box.
c. The volume of the smaller box is
of the volume of the larger box.
d. The volume of the smaller box is
of the volume of the larger box.
____ 14. Monica is building a chair for her front porch. She cuts each leg so that they form a 48° angle with the
base of the seat of the chair as shown in the diagram below.
What angle does the front of each leg make with the ground, x, in order to ensure that the seat of the
chair is parallel with the ground?
a. 48° b. 90° c. 122° d. 132°
____ 15. Which conjecture is NOT always true?
a. Intersecting lines form 4 pairs of adjacent angles.
b. Intersecting lines form 2 pairs of vertical angles.
c. Intersecting lines form 4 pairs of congruent angles.
d. none of the above
____ 16. What is the length of the hypotenuse?
a. 18 b. 12 c. 6 d. 5
____ 17. Given: ∠ CBF ≅ ∠ CDG , AC bisects ∠ BAD
Prove: AD ≅ AB
Complete the flowchart proof.
Proof:
∠ CBF ≅ ∠ CDG ∠ ABC ≅ ∠ ADC
Given 1.
AC bisects
∠ BAD
2. D ACB ≅ D ACD
AD ≅ AB
Given. Definition of
angle bisector.
AC ≅ AC
a. 1. Congruent Complements Theorem
2. ∠ ACB ≅ ∠ ACD
3. Transitive Property of Congruence
4. CPCTC
5. AAS
c. 1. Congruent Supplements Theorem
2. ∠ CAB ≅ ∠ CAD
3. Reflexive Property of Congruence
4. AAS
5. CPCTC
b. 1. Congruent Supplements Theorem
2. ∠ CAB ≅ ∠ CAD
3. Transitive Property of Congruence
4. AAS
5. CPCTC
d. 1. Congruent Complements Theorem
2. ∠ ACB ≅ ∠ ACD
3. Reflexive Property of Congruence
4. CPCTC
5. AAS
____ 20. Which coordinates are the vertices of a figure that is similar to the figure pictured below?
a. (–2 a , 0), (0, 2 c ), (2 b , 0), (0, –2 c ) c. (– a + 1, 0), (1, c ), ( b , 1), (0, – c + 1)
b. (
a , 0 ), ( 0 ,
c ), ( 2 b , 0 ), ( 0 , 2 c ) d. (2 a , 0), (0, 4 c ), (–2 b , 0), (0, 2 c )
____ 21. What is the missing reason in the two-column proof?
Given: MO
⎯⎯⎯ →
bisects ∠ PMN and OM
⎯⎯⎯ →
bisects ∠ PON
Prove: Δ PMO ≅ Δ NMO
Statements Reasons
1. MO
⎯⎯⎯ →
bisects ∠ PMN.
- Given
- ∠ PMO ≅ ∠ NMO 2. Definition of angle bisector
3. MO ≅ MO
- Reflexive Property of
Congruence
4. OM
⎯⎯⎯ →
bisects ∠ PON.
- Given
- ∠ POM ≅ ∠ NOM 5. Definition of angle bisector
6. Δ PMO ≅ Δ NMO 6.?
a. ASA Postulate c. AAS Theorem
b. AA Postulate d. SAS Postulate
____ 22. Which regular polyhedron has 12 petagonal faces?
a. dodecahedron
b. tetrahedron
c. icosahedron
d. cube
____ 25. Find AD.
a. 2 3 m
b. 3 3 m
c. 6 m
d. 6 3 m
____ 26. In the diagram below, m ∠ M = 44º and MN = 12 yards. What is the length of MP to the nearest tenth?
a. 8.6 yards c. 17 yards
b. 16.7 yards d. 17.3 yards
____ 27. Given that MON ∼ POQ , and coordinates P (−4, 0), M (−2, 0) and Q (0, −12), find the coordinates of N
and the scale factor of POQ to MON.
a. N (0, −6) and scale factor is 2.
b. N (0, −8) and scale factor is
c. N (−6, 0) and scale factor is 3.
d. N (0, −6) and scale factor is 1
____ 28. How many edges does a tetrahedron have?
a. 3
b. 6
c. 9
d. 12
____ 29. How do you write the contrapositive of the conditional statement below?
“If m ∠ 1 = 60 °, then ∠ 1 is acute.”
a. If m ∠ 1 = 60 °, then ∠ 1 is not acute.
b. If ∠ 1 is not acute, then m ∠ 1 ≠ 60 °.
c. If ∠ 1 is acute, then m ∠ 1 = 60 °.
d. If m ∠ 1 ≠ 60 °, then ∠ 1 is not acute.
____ 33. Given: ∠ B ≅ ∠ D
Which of the following conjectures can NOT be made based on the diagram and the given information?
a. AB Ä CD
b. AXB ∼ CXD
c. BD ⊥ AC
d. ∠ A ≅ ∠ C
____ 34. A rectangle has a perimeter of 14 inches. A similar rectangle has a perimeter of 42 inches. The area of
the smaller rectangle is 10 square inches. What is the area of the larger rectangle?
a. 3.3 square inches
b. 30.0 square inches
c. 38.0 square inches
d. 90.0 square inches
____ 35. Rob wants to take a picture of a fountain. His camera is at the vertex of the angle formed by the
tangents to the fountain. If Rob estimates that this angle is 30 °, what is the measure x of the arc of the
fountain that will be in the photograph?
a. 150 °
b. 140 °
c. 120 °
d. 100 °
____ 36. How many two inch cubes will fit inside the four inch cubic box?
a. 4 b. 6 c. 8 d. 16
____ 37. A low-wattage radio station can be heard only within a certain distance from the station. On the graph
below, the circular region represents that part of the city where the station can be heard, and the center
of the circle represents the location of the station. Which equation represents the boundary for the
region where the station can be heard?
a. ( x – 7)
2
2
= 4 c. ( x + 7)
2
2
b. ( x – 7)
2
2
= 2 d. ( x + 7)
2
2
____ 38. Two sides of a triangle are 11 centimeters and 14 centimeters. What are all possible values for the
length x of the third side?
a. x = 3 or x = 25
b. 3 < x < 25
c. x < 3 or x > 25
d. x = 14
____ 41. The net below represents an icosahedron. How many faces does an icosahedron have?
a. 10
b. 12
c. 15
d. 20
____ 42. What are the center and radius of the circle with equation ( x − 2 )
2
Ê
Ë
Á
Á
2
a. center ( 2 , − 5 ); radius 90 c. center (− 2 , 5 ); radius 36 5
b. center ( 2 , − 5 ); radius 6 5 d. center (− 2 , 5 ); radius 180
____ 43. Find the difference in the volume of the two spheres below.
a. 972 π c. 180 π
b. 684 π d. 324 π
____ 44. Which of the following graphs correctly displays the equation ( x − 4 )
2
Ê
Ë
Á
Á
2
a. c.
b. d.
____ 45. When writing a coordinate proof, which of the following would you use to prove that the diagonals of a
quadrilateral are congruent?
a. the slope formula c. the point-slope formula
b. the distance formula d. the midpoint formula
