GHSGT GEOMETRY PRACTICE TEST Name: ______

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1. / Find the midpoint between point G and point H.
A. / (-2, 2)
B. / (-1, 2)
C. / (1, -1)
D. / (-1, 1)

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2. / A mathematician made the table below.
Shape / Faces / Vertices / Edges
regular tetrahedron / 4 / 4 / 6
cube / 6 / 8 / 12
regular octahedron / 8 / 6 / 12
regular dodecahedron / 12 / 20 / 30
Based solely on the information in the table, she made the conjecture below.
If F represents the number of faces of a polyhedron, V represents the number of vertices, and E represents the number of edges then F + V = E + 2.
Which of the following did the mathematician use?
A. / mathematical proof
B. / deductive reasoning
C. / inductive reasoning
D. / counterexample

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3. / For which of the following statements is the inverse false?
A. / If an object is a cube with side length s, then its volume is calculated by s3.
B. / If an object is a cube, then it has eight vertices.
C. / If an object is a cube with side length s, then its surface area is calculated by 6s2.
D. / If an object is a cube, then it has six square faces.

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4. / Find the sum of the interior angles of a polygon with six sides.
A. / 720°
B. / 900°
C. / 1,080°
D. / 540°

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5. / Given the right triangle below, list the angles in order from greatest to least.
*Picture not drawn to scale.
A. / K, L, KMN
B. / KMN, L, K
C. / KMN, K, L
D. / L, K, KMN

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6. / If H K, which of the following conditions must also be met to prove that GHJ LKJ by Angle-Angle-Side rule?
I. / HJ KJ
II. / HJ LJ
III. / GH LK
IV. / GJ LJ
V. / JK JL
A. / I
B. / II
C. / III or IV
D. / I or V
7. / A quadrilateral has two right angles and only one set of parallel sides. Which of the following best identifies this quadrilateral?
A. / trapezoid
B. / square
C. / rhombus
D. / rectangle

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8. / Given the triangle PQR, a line that passes through the angle P and the midpoint of side p is called a(n) ______.
A. / altitude
B. / intersector
C. / bisector
D. / median

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9. / Robert sees a bird sitting on top of a telephone pole. He estimates the angle of elevation to the top of the pole to be 57°. If he is standing 20 feet from the base of the pole, about how tall is the telephone pole? (Assume the pole meets the ground at a right angle.)
A. / 11 feet
B. / 31 feet
C. / 13 feet
D. / 17 feet

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10. /
*Note: Picture not drawn to scale.
If the measure of = 136°, what is the measure of R?
A. / 88°
B. / 224°
C. / 44°
D. / 46°

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11. / A sphere has a diameter of 6 units. If the diameter is increased to 12 units, how is the volume of the original sphere affected?
A. / The volume is multiplied by 216.
B. / The volume is multiplied by 2.
C. / The volume is multiplied by 8.
D. / The volume is multiplied by 6.

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12. / The point (2,9) lies on a circle and the center of the circle is at the point (1,9).
What is the equation of this circle?
A. / (x + 1)2 + (y + 9)2 = 1
B. / (x - 1)2 + (y - 9)2 = 1
C. / (x - 9)2 + (y - 1)2 = 1
D. / (x - 1)2 - (y - 9)2 = 1

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13. / What is the distance between the points (-3, 19) and (12, 19) in the xy-plane?
A. / 7.5 units
B. / 15 units
C. / 9 units
D. / 7 units

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14. / (6, 3) is the midpoint between (3, 4) and (x2, y2). Find (x2, y2).
A. / (9, 2)
B. / (12, 6)
C. / (-3, 1)
D. / (7, -3)
E. / (9, 7)

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15. / Given: / rhombus PQRS with diagonals PR and QS intersecting at point C
Prove: / PQS RQS
and
PSQ RSQ
Statements / Reason
1) PQRS is a rhombus / Given
2) PQ RQ and PS RS / Definition of a rhombus
3) QS QS / Reflexive property
4) SPQ SRQ / ASA congruence
5) / PQS RQS
PSQ RSQ
/ Corresponding parts of congruent triangles are congruent
Critique the proof above to determine which of the following is true.
A. / Reason 3 should be transitive property.
B. / The conclusion is incorrect since PQS RQS.
C. / The proof is correct.
D. / Reason 4 should be SSS congruence.

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16. / What is the converse of the statement below?
If an angle is greater than 90°, then it is obtuse.
A. / If an angle is not greater than 90°, then it is not obtuse.
B. / If an angle is not obtuse, then it is not greater than 90°.
C. / If an angle is obtuse, then it is greater than 90°.
D. / If an angle is obtuse, then it is not greater than 90°.

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17. / The interior angles of a polygon equal 1,440°. How many sides does this polygon have?
A. / 11
B. / 10
C. / 12
D. / 9

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18. / Given right triangle PQR, and mR = 65°, list the sides in order from the least to the greatest.
A. / RP, QR, PQ
B. / RP, PQ, QR
C. / PQ, QR , RP
D. / PQ, QR, RP

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19. / Which of the following figures uses the HL theorem to show that RST UVW?
W. /
X.
Y. /
Z.
A. / W
B. / X
C. / Y
D. / Z

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20. / Given: / ABCD and FECG are parallelograms.
Prove: / 1 3
Proof:
Statements / Reasons
1. ABCD and FECG are parallelograms. / 1. Given
2. 1 2 and 2 3 / 2.
3. 1 3 / 3. Transitive Property of Congruence
Which reason completes the proof?
A. / Alternate Interior Angles theorem
B. / Opposite angles of a parallelogram are congruent.
C. / Opposite sides of a parallelogram are congruent.
D. / Alternate Interior Angles Converse

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21. / Which of the following is always the center of the circle inscribed in a triangle?
A. / the point of concurrency of the triangle's angle bisectors
B. / the point of concurrency of the triangle's medians
C. / the point of concurrency of the triangle's altitudes
D. / the point of concurrency of the perpendicular bisectors of the triangle's sides

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22. / The lamp in the study illuminates an area that is 12 feet diagonally at an angle of 40° from the ground to the top of the lamp.
Note: picture not drawn to scale
Which equation can be used to find the horizontal length, r, of the illuminated area?
A.
B.
C.
D.

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23. /
Note: picture not drawn to scale
If m = 38° and mBCD = 23°, what is m?
A. / 61°
B. / 107°
C. / 84°
D. / 38°

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24. / A sphere has a radius of 21 units. If the radius is decreased to 7 units, how is the volume of the original sphere affected?
A. / The volume is multiplied by 1/3.
B. / The volume is multiplied by 1/9.
C. / The volume is multiplied by 1/27.
D. / The volume is multiplied by 1/42.

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25. / The point (4,14) lies on a circle and the center of the circle is at the point (4,5).
What is the equation of this circle?
A. / (x - 5)2 + (y - 4)2 = 81
B. / (x - 4)2 + (y - 5)2 = 81
C. / (x + 4)2 + (y + 5)2 = 81
D. / (x - 5)2 - (y - 4)2 = 9

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26. / What is the distance between the points (5, 9) and (-3, 4) in the xy-plane?
A.
B.
C.
D.

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27. / Find the midpoint between point C and point D.
A. / (1.5, -6)
B. / (1.5, -3)
C. / (3, -6)
D. / (2.5, -3)

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28. / Consider the following conjecture concerning two quadrilaterals A and B.
If the area of quadrilateral A is larger than the area of quadrilateral B, then the perimeter of quadrilateral A is larger than the perimeter of quadrilateral B.
Determine whether the conjecture above is true or false. If the statement is false, determine which of the counterexamples provided show that the conjecture is false?
A. / The conjecture is false. Counterexample: a 2×8 rectangle and a 3×5 rectangle
B. / The conjecture is true and can be proven.
C. / The conjecture is false. Counterexample: a 4×4 square and a 1×15 rectangle
D. / The conjecture is false. Counterexample: a 5×10 rectangle and a 7×7 rectangle

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29. / What is the converse of the statement below?
If a quadrilateral has four right angles,
then it is a rectangle.
A. / If a quadrilateral is a rectangle,
then it does not have four right angles.
B. / If a quadrilateral is not a rectangle,
then it does not have four right angles.
C. / If a quadrilateral does not have four right angles,
then it is not a rectangle.
D. / If a quadrilateral is a rectangle,
then it has four right angles.

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30. / A convex figure has six sides. What is the sum of its exterior angles?
A. / 630°
B. / 270°
C. / 450°
D. / 360°

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31. / In the scalene triangle below, mA = 47°.
What must be true in the triangle?
A. / mBCD = mA
B. / mBCD + mA = 180°
C. / mBCD < mA
D. / mBCD > mA

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32. / James drew the following triangles to show that ABC LMN by the AAS corollary. Does James's drawing prove congruence by the AAS corollary?
A. / Yes, one side of the two triangles is congruent.
B. / Yes, James's drawing shows that one side and two angles of each triangle are congruent.
C. / No, James did not mark enough congruent sides.
D. / No, James marked the included sides congruent.

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33. / Given rectangle GHJK, what would be the reason(s) that GHJK is a square?
I.  four right angles
II.  four sides are congruent
III. only one pair of parallel sides
A. / I and II
B. / I only
C. / I, II, and III
D. / II only

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34. / A ______is a line or segment that passes through the midpoint of a side of a triangle and is perpendicular to that side.
A. / perpendicular bisector
B. / mode
C. / angle bisector
D. / median

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35. / In the above triangle, if x = 1, y = 1, and z = , then which of the following is equal to cos(45°)?
A.
B.
C.
D.

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36. / The measure of arc MP is 68°.
What is the measure of MAP?
A. / 112°
B. / 34°
C. / 68°
D. / 136°

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37. / A sphere has a diameter of 32units. If the diameter is decreased to 8units, how is the surface area of the original sphere affected?
A. / The surface area is multiplied by 1/4.
B. / The surface area is multiplied by 1/16.
C. / The surface area is multiplied by 4.
D. / The surface area is multiplied by 1/8.

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38. / The point (6,14) lies on a circle and the center of the circle is at the point (6,4).
What is the equation of this circle?
A. / (x - 4)2 + (y - 6)2 = 100
B. / (x + 6)2 + (y + 4)2 = 100
C. / (x - 4)2 - (y - 6)2 = 10
D. / (x - 6)2 + (y - 4)2 = 100

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39. / What is the distance between the points (-3, 19) and (6, 19) in the xy-plane?
A. / 13 units
B. / 22 units
C. / 4.5 units
D. / 9 units

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40. / (0, -5) is the midpoint between (-3, -3) and (x2, y2). Find (x2, y2).
A. / (0, -10)
B. / (-3, -8)
C. / (-3, 2)
D. / (3, -7)
E. / (1, -5)

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41. / What is the most specific name for figure ABC?
A. / scalene
B. / equilateral
C. / isosceles
D. / right

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42. / What is the inverse of the statement below?
If the perimeter of a square is 20 cm, then its area is 25 cm2.
A. / If the perimeter of a square is not 20 cm, then its area is 25 cm2.
B. / If the area of a square is not 25 cm2, then its perimeter is not 20 cm.
C. / If the area of a square is 25 cm2, then its perimeter is 20 cm.
D. / If the perimeter of a square is not 20 cm, then its area is not 25 cm2.

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43. / A polygon with nine sides has the following interior angle measurements:
56°, 241°, 143°, 70°, 87°, 269°, 87°, 192°, and x°
What is the value of x?
A. / 297
B. / 295
C. / 115
D. / 168

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44. / Based on the isosceles triangle below, which statement is true?
*Picture not drawn to scale.
A. / The measures of RHM and BAM are both greater than the measure of M.
B. / The measures of RHM and BAM are both less than the measure of M.
C. / The measure of RHM is greater than the measure of M, but the measure of BAM is less than the measure of M.
D. / The measure of RHM is less than the measure of M, but the measure of BAM is greater than the measure of M.

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