Geometry Practice

Welcome to the Geometry full exam practice test. This test is one question at a time. Good luck!

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Part I: Multiple Choice

1. An equilateral triangle is continuously rotated around one of its altitudes. The three-dimensional object formed is a

cone sphere cylinder pyramid

2. On the set of axes (see PDF for diagram), quadrilateral BDGF is rotated 90 degrees clockwise about the origin and then reflected over the y-axis. The image of quadrilateral BDGF is quadrilateral MQSP. Side BD will always map onto

MP PS MQ SQ

3. In right triangle JOE, hypotenuse JO = 31.8 and m∠J = 38°. To the nearest tenth, the length of EJ is

19.6 25.1 40.4 51.7

4. The hemisphere below (see PDF for diagram) has a radius of 8 cm. To the nearest cubic centimeter, the volume of the hemisphere is

201 268 1072 2145

5. In parallelogram ABCD, diagonals AC and BD intersect at E. Which information is sufficient to prove ABCD is a rhombus?

AE ≅ EC AC ≅ BD AB ⊥ BC AC ⊥ BD

6. Trapezoid JOSH, shown below (see PDF for diagram), has parallel sides HS and JO. m∠J = 65°, m∠O = 30°, m∠OSA = 80°, and m∠SHU = 60°. What is m∠HSA?

55° 60° 65° 70°

7. In ΔABC below (see PDF for diagram), points D and E are on AB and CB, respectively, such that DE || AC. If AD = 8, DB = 4, and DE = 6, what is the length of AC?

24 18 12 10

8. On the set of axes below (see PDF for diagram), circle C has a center with coordinates (2, -1) and a radius that passes through (2, 4). Which equation represents circle C?

(x - 2)² + (y + 1)² = 25 (x - 2)² + (y + 1)² = 16 (x + 2)² + (y - 1)² = 25 (x + 2)² + (y - 1)² = 16

9. On the set of axes below (see PDF for diagram), ΔD'E'F' is the image of ΔDEF. A transformation that maps ΔDEF onto ΔD'E'F' is a

reflection over the line y = x reflection over the line y = -x point reflection through the origin translation 4 units left and 4 units down

10. In circle O below (see PDF for diagram), secants PCA and PDB are drawn from external point P. If PA = 17, PD = 10, and BD = 12, what is the length of PC to the nearest tenth?

7.1 7.7 12.9 14.2

11. In the diagram below (see PDF), CD || AB and CB bisects ∠ABD. Which statement must be true?

CD ≅ AB AB ≅ BD ΔCDB is a right triangle ΔCDB is an isosceles triangle

12. Line h is represented by the equation y = (2/3)x - 4. Which equation represents the line that is perpendicular to line h and passes through the point (6, 1)?

y - 1 = (2/3)(x - 6) y + 1 = (2/3)(x + 6) y - 1 = - (3/2)(x - 6) y + 1 = - (3/2)(x + 6)

13. A wooden toy block (see PDF) is a pyramid with a square base. The height is 17.4 cm and the base side length is 8.2 cm. The density of oak is 0.77 g/cm³. What is the mass of the block, to the nearest gram?

300 506 637 901

14. In ΔABC below (see PDF), midsegment DE is drawn. If DE = x + 3 and AC = 3x - 5, what is the length of DE?

28 14 7 4

15. Triangle DUG is an isosceles right triangle with the right angle at G. If DU = 10√2, what is the length of GU?

5 5√2 10 10√2

16. In ΔRST below (see PDF), RS = 9 cm, RT = 8 cm, and m∠TRS = 55°. What is the area of ΔRST, to the nearest square centimeter?

59 36 29 21

17. Triangle ABC is dilated by a scale factor of 2 to map onto its image, ΔRST, on the set of axes below (see PDF). What are the coordinates of the center of this dilation?

(1, -1) (2, 1) (3, 3) (0, 0)

18. What is the perimeter of ΔABC where the vertices have coordinates A(-2, 3), B(-2, -1), and C(6, -1)?

16 92 16√5 12 + 4√5

19. In the diagram below (see PDF), GT and PF intersect at E, and ∠P ≅ ∠F. Which equation is always true?

PE/FE = FT/PG GE/TE = FT/PG PE/GE = TE/FE PE/FE = PG/FT

20. A section of sidewalk is 10 feet long, 4 feet wide, and 4 inches deep. Concrete mix yields 0.6 cubic foot per bag. What is the minimum number of bags needed?

22 23 26 27

21. The line 4x - 6y = 24 is transformed by a dilation of scale factor 3 centered at the origin. Which equation represents the image of the line?

y = (2/3)x - 12 y = (2/3)x - 4 y = 2x - 12 y = 2x - 4

22. A rhombus is graphed on the set of axes below (see PDF). Which transformation does not carry the rhombus onto itself?

a rotation of 180° about the origin a rotation of 180° about point (1, 0) a reflection over the line y = (1/2)x - 1/2 a reflection over the line y = -2x + 2

23. In right triangle HAY below (see PDF), altitude AL is drawn to hypotenuse HY. If HY = 25 and YA = 20, the length of AL is

9 12 15 16

24. Square ABCD has an area of 36. If the square is dilated by a scale factor of 1/2 centered at A, what is the area of its image?

9 18 72 144

25. Triangle D'A'N' is the image of ΔDAN after a translation. Explain why ΔD'A'N' must be congruent to ΔDAN.

Your explanation:

26. The table (see PDF) lists five metals and their densities. A solid metal cube has an edge length of 5 cm and a mass of 982.5 grams. Determine and state the type of metal.

Your answer (Metal name):

27. The endpoints of CS are C(-3, 1) and S(7, 6). Determine and state the coordinates of point A such that the ratio of CA:AS is 3:2.

Your answer (e.g., (x,y)):

28. The ramp shown in the diagram (see PDF) has an angle of elevation of 4.8°. The ramp is built to a landing 0.6 m above the ground. Determine and state the length of the ramp, to the nearest tenth of a meter.

Your answer (in meters):

29. Angle KML is the vertex angle of isosceles triangle KLM (see PDF). Side LM is extended through vertex M to point N. If m∠K = 15°, determine and state m∠KMN.

Your answer (in degrees):

30. In the diagram of circle L (see PDF), the area of the shaded sector KLM is 7.5π and LK = 5. Determine and state the degree measure of angle KLM.

Your answer (in degrees):

31. (For Review) Using a compass and straightedge, construct the image of point A after a reflection over BC. [Leave all construction marks.]

This question requires a geometric construction and will not be graded by the script. Please check your construction against the answer key.

32. Joan wants to fill an empty 75-liter fish tank. She uses a cylindrical bucket with a diameter of 20 cm. Determine and state the maximum number of buckets of water, filled to a height of 26 cm, she can put in before it overflows. [1000 cm³ = 1 liter]

Max number of buckets:

33. As modeled in the diagram (see PDF), two cables are attached to a tree 12 ft above ground. The longer cable is anchored 3 ft farther from the tree than the shorter cable. The angle of elevation for the shorter cable is 50°.

Determine, to the nearest foot, the distance from the base of the tree to where the longer cable is attached. Determine, to the nearest degree, the angle of elevation for the longer cable.

34. (For Review) Quadrilateral READ has vertices R(-1, 3), E(2, 7), A(10, 1), and D(7, -3). Prove READ is a rectangle.

This question requires a coordinate proof and will not be graded by the script. Please check your proof against the answer key.

35. (For Review) In the diagram (see PDF), side CD is extended to E. Segments AFD and BFE bisect each other, and DE ≅ DC. Prove ABCD is a parallelogram.

This question requires a geometric proof and will not be graded by the script. Please check your proof against the answer key.