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Geometry Final Exam Study Guide

Short Answer

1. Find the geometric mean between each pair of numbers.256 and 841

2. Find x.

Determine whether ΔQRS is a right triangle for the given vertices. Explain.

3. Q(18, 13), R(17, –3), S(–18, 12) 4. Find x and y.

5. Find x and y.

6. Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest ten-thousandth.

AC = 5 5 , CB = 5 , AD = 11, CD = 2, DB = 1

cos B 7. Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed by the ground and the

line segment from her position to the top of the building is 15.7°. The height of the Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot.

ID: A

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A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

8. During one stage of the drawbridge’s motion, the raised end is 15 yards above the ground. What is the incline of the drawbridge to the nearest hundredth?

9. A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2° and 8.7°. How far apart are the cars?

Find each measure using the given measures of ΔKLM. Round angle measures to the nearest degree and side measures to the nearest tenth.

10. If m∠L = 47.1, k = 59.6, and l = 52.2, find m∠K. 11. David and his friends are building a fort on a triangular plot of land. They want to dig a moat around the fort. The length of one

side of the plot of land is 27 feet. If the angles at the end of this side are 45° and 75°, find the length of the moat that will enclose the entire plot of land on which the fort is built.

12. In ΔDEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree.d = 5.4, e = 10.5, f = 10.8; m∠F

Members of the soccer team are trying to map out some new plays before their next game. The goal is 24 feet wide.

13. Pedro came up with a play that would put him 35 feet from one goal post and 45 feet from the other post. What is his angle to make a shot on goal?

14. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if necessary. 15. Find the measure of an exterior angle of a regular polygon with 20 sides. Round to the nearest tenth if necessary.

Complete the statement about parallelogram ABCD.

16. AD ≅

Refer to parallelogram ABCD to answer to following questions.

17. What is the distance between points A and C?

ID: A

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Determine whether the quadrilateral is a parallelogram. Justify your answer.

18.

Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

19. A(3, − 9), B(10, 1), C(4, 10), D(−9, 3); Distance and Slope Formulas

Quadrilateral ABCD is a rectangle.

20. If ∠ADB = 2y+ 40 and ∠CDB = −3y+ 51, find ∠CBD.

21.

In rhombus TUVW , if m∠TUW = 34, find m∠UVT.

Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply.

22. A(−2, 6), B(−2, − 1), C(−9, − 1), D(−9, 6)

23. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.

ID: A

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The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary.

24. d = 22.3 km, r =  ? , C =  ? 25. Find the exact circumference of the circle.

Use the diagram to find the measure of the given angle.

26. m∠BAF

27.

If m∠1 = 2x + 2, m∠2 = 9x, find m∠1.

ID: A

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28. Find x. Assume that segments that appear tangent are tangent.

29. Find x. Assume that segments that appear tangent are tangent.

Find the measure of the numbered angle.

30.

ID: A

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Find x. Assume that any segment that appears to be tangent is tangent.

31.

32. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.

Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle or a parallelogram. Then find the area of the quadrilateral.

33. E(0, –2), F(3, –2), G(–2, 3), H(1, 3) 34. Find the area of the figure. Round to the nearest tenth if necessary.

35. Find the area of the figure. Round to the nearest tenth if necessary.

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36. Find the area of the figure. Round to the nearest tenth if necessary.

Find the area of the figure. Round to the nearest tenth if necessary.

37.

38.

Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer.

39.

Find the lateral area of a cylinder with the given measurements. Use 3.14 for pi and round your answer to the nearest tenth.

40. height: 18 inchesradius: 9 inches

ID: A

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Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth.

41.

42. Each side of the square base of a regular pyramid is 6.9 feet. The sides rise at an angle of 52°. Find the lateral area of the pyramid. Round to the nearest tenth.

Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.

43.

44. Find the lateral area of a cone if the height is 12 meters and the slant height is 16 meters. Use 3.14 for π. Round to the nearest tenth if necessary.

Find the slant height of the cone with the given measurements, rounded to the nearest hundredth. Then use your result to find the surface area of the cone. Use 3.14 for π. Round the final answer to the nearest ten-thousandth.

45. height: 8 yardsdiameter: 8 yards

Determine whether each statement is true or false. If false, give a counterexample.

46. If a plane intersects a sphere so that it contains the center of the sphere, then that intersection will sometimes be a great circle. 47. Find the surface area of a sphere if the circumference of a great circle is 43.96 centimeters. Use 3.14 for π. Round to the nearest

tenth.

ID: A

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Find the volume of the prism. Round to the nearest tenth if necessary.

48.

Find the volume of the cylinder. Use 3.14 for π. Round to the nearest tenth.

49.

Find the volume of the solid formed by the net. Use 3.14 for π when needed. Round to the nearest tenth.

50.

Find the volume of the pyramid. Round to the nearest tenth if necessary.

51.

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Find the volume of the cone. Use 3.14 for π. Round to the nearest tenth.

52.

53. Find the volume of the sphere. Use 3.14 for π. Round to the nearest tenth.

ID: A

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Geometry Final Exam Study GuideAnswer Section

SHORT ANSWER

1. ANS: 4 29

OBJ: 7-1.1 Find the geometric mean between two numbers. 2. ANS:

2 286

OBJ: 7-2.1 Use the Pythagorean Theorem. 3. ANS:

no; QR = 257 , QS = 1297 , RS = 5 58 ; QR2 + QS2 ≠ RS2

OBJ: 7-2.2 Use the converse of the Pythagorean Theorem. 4. ANS:

x = 45°, y = 13.1 2

OBJ: 7-3.1 Use properties of 45º-45º-90º triangles. 5. ANS:

x = 1.5, y = 1.5 3

OBJ: 7-3.2 Use properties of 30º-60º-90º triangles. 6. ANS:

0.4472

OBJ: 7-4.1 Find trigonometric ratios using right triangles. 7. ANS:

5159 feet

OBJ: 7-4.2 Solve problems using trigonometric ratios. 8. ANS:

14.48°

OBJ: 7-5.1 Solve problems involving angles of elevation. 9. ANS:

58.6 m

OBJ: 7-5.2 Solve problems involving angles of depression. 10. ANS:

56.7

OBJ: 7-6.1 Use the Law of Sines to solve triangles. 11. ANS:

79.1 ft

OBJ: 7-6.2 Solve problems by using the Law of Sines. 12. ANS:

78

OBJ: 7-7.1 Use the Law of Cosines to solve triangles.

ID: A

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13. ANS: 31.9

OBJ: 7-7.2 Solve problems by using the Law of Cosines. 14. ANS:

154.3

OBJ: 8-1.1 Find the sum of the measures of the interior angles of a polygon. 15. ANS:

18

OBJ: 8-1.2 Find the sum of the measures of the exterior angles of a polygon. 16. ANS:

BC; Opposite sides of parallelograms are congruent.

OBJ: 8-2.1 Recognize and apply properties of the sides and angles of parallelograms. 17. ANS:

6 2

OBJ: 8-2.2 Recognize and apply properties of the diagonals of parallelograms. 18. ANS:

no; Opposite angles are not congruent.

OBJ: 8-3.1 Recognize the conditions that ensure a quadrilateral is a parallelogram. 19. ANS:

no; The opposite sides are not congruent and do not have the same slope.

OBJ: 8-3.2 Prove that a set of points forms a parallelogram in the coordinate plane. 20. ANS:

42

OBJ: 8-4.1 Recognize and apply properties of rectangles. 21. ANS:

56

OBJ: 8-5.1 Recognize and apply the properties of rhombi. 22. ANS:

square; rectangle; rhombus

OBJ: 8-5.2 Recognize and apply the properties of squares. 23. ANS:

40

OBJ: 8-6.1 Recognize and apply the properties of trapezoids. 24. ANS:

r = 11.15 km, C = 70.06 km

OBJ: 10-1.1 Identify and use parts of circles. 25. ANS:

12π 2 mm

OBJ: 10-1.2 Solve problems involving the circumference of a circle. 26. ANS:

50

OBJ: 10-2.1 Recognize major arcs¸ minor arcs¸ semicircles¸ and central angles and their measures.

ID: A

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27. ANS: 18

OBJ: 10-4.1 Find measures of inscribed angles. 28. ANS:

6

OBJ: 10-5.1 Use properties of tangents. 29. ANS:

11

OBJ: 10-5.2 Solve problems involving circumscribed polygons. 30. ANS:

65

OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle. 31. ANS:

40

OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle. 32. ANS:

16 mm; 15.4 mm2

OBJ: 11-1.1 Find areas of parallelograms. 33. ANS:

parallelogram, 15 units2

OBJ: 11-1.2 Determine whether a set of points defines a quadrilateral. 34. ANS:

36.4 m2

OBJ: 11-2.1 Find areas of triangles. 35. ANS:

97.1 mm2

OBJ: 11-2.2 Find areas of trapezoids. 36. ANS:

672 in2

OBJ: 11-2.3 Find areas of rhombi. 37. ANS:

41.5 units2

OBJ: 11-4.2 Find areas of irregular figures on the coordinate plane. 38. ANS:

199.3 units2

OBJ: 11-4.1 Find areas of irregular figures. 39. ANS:

164 units2

OBJ: 12-3.2 Find surface areas of prisms.

ID: A

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40. ANS: 1017.4 in2

OBJ: 12-4.1 Find lateral areas of cylinders. 41. ANS:

650.2 cm2

OBJ: 12-4.2 Find surface areas of cylinders. 42. ANS:

77.3 feet2

OBJ: 12-5.1 Find lateral areas of regular pyramids. 43. ANS:

496.7 yd2

OBJ: 12-5.2 Find surface area of regular pyramids. 44. ANS:

531.7 meters2

OBJ: 12-6.1 Find lateral areas of cones. 45. ANS:

162.5264 yards2

OBJ: 12-6.2 Find surface area of cones. 46. ANS:

False, the intersection will always be a great circle.

OBJ: 12-7.1 Recognize and define basic properties of spheres. 47. ANS:

615.4 cm2

OBJ: 12-7.2 Find surface area of spheres. 48. ANS:

437.1 cm3

OBJ: 13-1.1 Find volumes of prisms. 49. ANS:

12,258.6 in3

OBJ: 13-1.2 Find volumes of cylinders. 50. ANS:

12.9 ft3

OBJ: 13-1.3 Find volumes of solids. 51. ANS:

1874.6 yd3

OBJ: 13-2.1 Find volumes of pyramids. 52. ANS:

628.0 m3

OBJ: 13-2.2 Find volumes of circular cones.

ID: A

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53. ANS: 2,571.1 m3

OBJ: 13-3.1 Find volumes of spheres.