Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry B Final

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

1.

2. Two sides of a triangle have lengths 7 and 17. Which expression describes the length of the third side?A. at least 10 and less than 24B. greater than 10 and at most 24C. at least 10 and at most 24D. greater than 10 and less than 24

3. The area of a square garden is 98 m2. How long is the diagonal?

4. Find the measure of BAC in circle O. (The figure is not drawn to scale.)

5. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.

6. 7.

Name: ________________________ ID: A

2

8. Name a median for ABC.

Find the value of x. Round to the nearest degree.

9. 10. A kite has diagonals 6.5 ft and 10 ft. What is the area of the kite?

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

11.

Name: ________________________ ID: A

3

Find the area. The figure is not drawn to scale.

12. 13.

Find the area of the trapezoid. Leave your answer in simplest radical form.

14.

15. Use Euler’s Formula to find the missing number.Vertices: 15Edges: 33Faces: ?

16. The length of DE is shown. What other length can you determine for this diagram?

A. EF = 15B. DF = 30C. DG = 15D. No other length can be determined.

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.

17.

Name: ________________________ ID: A

4

18. In circle Z, BZ FZ , BZ CA, FZ DC , DF = 48 in.What is BC?

19. Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale.

Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.

20. 21. Find the area of the regular polygon. Round your answer to the nearest tenth.

Name: ________________________ ID: A

5

22. What are the minor arcs of O?

Use the Law of Cosines to find the missing angle.

23. In FGH , g = 10 ft, h = 20 ft, and mF = 62°. Find the measure of f. Round your answer to the nearest whole number.

24. Write the tangent ratios for P and Q.

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.

25. 26. A triangle has sides of lengths 36, 142, and 147. Is it a right triangle? Explain.

Find the value of x. Round to the nearest tenth.

27. 28.

Name: ________________________ ID: A

6

Find the area of the circle. Leave your answer in terms of .

29.

Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.

30.

31.

32. Find the area of the rhombus.

33. Name the point of concurrency of the angle bisectors.

Name: ________________________ ID: A

7

Find the circumference. Leave your answer in terms of .

34.

35. The area of a regular hexagon is 35 in.2 Find the length of a side. Round your answer to the nearest tenth.

36. In ACE, G is the centroid and BE = 18. Find BG and GE.

Find the area of the regular polygon. Give the answer to the nearest tenth.

37. hexagon with a side of 12 yd

38. Find the slant height of the cone to the nearest whole number.

39. Where can the perpendicular bisectors of the sides of a right triangle intersect? I. inside the triangleII. on the triangleIII. outside the triangleA. I onlyB. II onlyC. I or II onlyD. I, II, or II

40. AB is tangent to circle O at B. Find the length of the radius r for AB = 6 and AO = 9.9. Round to the nearest tenth if necessary. The diagram is not to scale.

Name: ________________________ ID: A

8

41. Find the value of x and y rounded to the nearest tenth.

42. Find the length of the midsegment. The diagram is not to scale.

43. Find the value of x.

44. A triangle has side lengths of 28 in, 25 in, and 43 in. Classify it as acute, obtuse, or right.

Find the length of the missing side. Leave your answer in simplest radical form.

45. 46. DF

bisects EDG. Find the value of x. The diagram is not to scale.

Name: ________________________ ID: A

9

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

47. mP 14

Find the length of the missing side. The triangle is not drawn to scale.

48. 49. What is the height h of the parallelogram?

Not drawn to scale

Find the value of x. Round the length to the nearest tenth.

50.

Name: ________________________ ID: A

10

Find the surface area of the cylinder in terms of .

51. 52. Which diagram shows a point P an equal distance from points A, B, and C?A.

B.

C.

D.

Name: ________________________ ID: A

11

53. Name the smallest angle of ABC. The diagram is not to scale.

A. BB. CC. AD. Two angles are the same size and smaller than

the third.

ID: A

1

Geometry B FinalAnswer Section

1. ANS:

7 3

PTS: 1 DIF: L2 REF: 8-2 Special Right TrianglesOBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One SideKEY: special right triangles | leg | hypotenuse

2. ANS: D PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c TOP: 5-6 Problem 5 Finding Possible Side LengthsKEY: Triangle Inequality Theorem

3. ANS: 14 m

PTS: 1 DIF: L4 REF: 8-2 Special Right TrianglesOBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 3 Finding Distance KEY: special right triangles | diagonal

4. ANS: 27.5

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.1 To find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.3| CC G.C.4| G.3.hTOP: 12-3 Problem 1 Using the Inscribed Angle Theorem KEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationship

5. ANS:

5 2

PTS: 1 DIF: L3 REF: 8-2 Special Right TrianglesOBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 2 Finding the Length of a Leg KEY: special right triangles | hypotenuse | leg

6. ANS:

47.1 cm2

PTS: 1 DIF: L2 REF: 10-5 Trigonometry and AreaOBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometryNAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 3 Finding AreaKEY: area of a triangle | area | sine

ID: A

2

7. ANS:

10.5 m2

PTS: 1 DIF: L3 REF: 10-5 Trigonometry and AreaOBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometryNAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 3 Finding AreaKEY: area of a triangle | area | sine

8. ANS:

BD

PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 5-4.1 To identify properties of medians and altitudes of a triangle NAT: CC G.CO.10| G.3.c TOP: 5-4 Problem 2 Identifying Medians and AltitudesKEY: median of a triangle

9. ANS: 47

PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 3 Using Inverses KEY: sine

10. ANS: 32.5 ft2

PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and KitesOBJ: 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1TOP: 10-2 Problem 3 Finding the Area of a Kite KEY: area | kite

11. ANS:

693 ft3

PTS: 1 DIF: L2 REF: 11-4 Volumes of Prisms and CylindersOBJ: 11-4.1 To find the volume of a prism and the volume of a cylinder NAT: CC G.GMD.1| CC G.GMD.2| CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.fTOP: 11-4 Problem 1 Finding the Volume of a Rectangular Prism KEY: volume of a rectangular prism | volume formulas | volume | prism

12. ANS:

29.76 cm2

PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and TrianglesOBJ: 10-1.1 To find the area of parallelograms and triangles NAT: CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-1 Problem 1 Finding the Area of a Parallelogram KEY: area | parallelogram | base | height

ID: A

3

13. ANS: 37.5 cm2

PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and TrianglesOBJ: 10-1.1 To find the area of parallelograms and triangles NAT: CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-1 Problem 3 Finding the Area of a Triangle KEY: triangle | area

14. ANS: 70 in.2

PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and KitesOBJ: 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1TOP: 10-2 Problem 1 Area of a Trapezoid KEY: trapezoid | area

15. ANS: 20

PTS: 1 DIF: L3 REF: 11-1 Space Figures and Cross SectionsOBJ: 11-1.1 To recognize polyhedra and their parts NAT: CC G.GMD.4| G.1.d| G.1.e| G.1.f| G.4.cTOP: 11-1 Problem 2 Using Euler's Formula KEY: polyhedron | face | vertex | edge

16. ANS: A PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c TOP: 5-2 Problem 1 Using the Perpendicular Bisector Theorem KEY: equidistant | perpendicular bisector | Perpendicular Bisector Theorem

17. ANS:

240 m2 ; 510 m2

PTS: 1 DIF: L2 REF: 11-2 Surface Areas of Prisms and CylindersOBJ: 11-2.1 To find the surface area of a prism and a cylinder NAT: CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-2 Problem 2 Using Formulas to Find Surface Area of a Prism KEY: surface area formulas | lateral area | surface area | prism | surface area of a prism

18. ANS: 48 in.

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 To use perpendicular bisectors to chords NAT: CC G.C.2| G.3.hTOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle | radius | chord | congruent chords | bisected chords

19. ANS: 48

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c TOP: 5-1 Problem 3 Using a Midsegment of a TriangleKEY: midsegment | Triangle Midsegment Theorem | problem solving

ID: A

4

20. ANS: 57

PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.1 To use congruent chords, arcs, and central angles NAT: CC G.C.2| G.3.hTOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | central angle | congruent arcs | chord

21. ANS: 483.0 in.2

PTS: 1 DIF: L3 REF: 10-3 Areas of Regular PolygonsOBJ: 10-3.1 To find the area of a regular polygon NAT: CC G.CO.13 | CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-3 Problem 3 Using Special Triangles to Find Area KEY: regular polygon | area | apothem | radius | octagon

22. ANS:

AB, BC , CD, and DA

PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.1 To find the measures of central angles and arcs NAT: CC G.CO.1| CC G.C.1| CC G.C.2| CC G.C.5 TOP: 10-6 Problem 1 Naming ArcsKEY: major arc | minor arc | semicircle

23. ANS: 17

PTS: 1 DIF: L3 REF: 8-6 Law of Cosines OBJ: 8-6.1 To apply the Law of Cosines NAT: CC G.SRT.10| CC G.SRT.11TOP: 8-6 Problem 1 Using the Law of Cosines (SAS) KEY: Law of Cosines

24. ANS:

tan P 512

; tan Q 125

PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 1 Writing Trigonometric Ratios KEY: tangent

25. ANS:

905 cm3

PTS: 1 DIF: L3 REF: 11-6 Surface Areas and Volumes of SpheresOBJ: 11-6.1 To find the surface area and volume of a sphere NAT: CC G.GMD.3| CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-6 Problem 3 Finding the Volume of a Sphere KEY: volume of a sphere | sphere | volume formulas | volume

ID: A

5

26. ANS:

no; 362 1422 1472

PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.1 To use the Pythagorean theorem and its converse NAT: CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.dTOP: 8-1 Problem 4 Identifying a Right Triangle KEY: Pythagorean Theorem | Pythagorean triple

27. ANS: 9.5

PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: cosine

28. ANS: 9.2

PTS: 1 DIF: L3 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: sine

29. ANS: 1.69 m2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 To find the areas of circles, sectors, and segments of circlesNAT: CC G.C.5 TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: area of a circle | radius

30. ANS: 5.2

PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: tangent

31. ANS: 13.9

PTS: 1 DIF: L2 REF: 8-3 Trigonometry OBJ: 8-3.1 To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles NAT: CC G.SRT.7| CC G.SRT.8| CC G.MG.1 TOP: 8-3 Problem 2 Using a Trigonometric Ratio to Find Distance KEY: tangent

ID: A

6

32. ANS: 98 m2

PTS: 1 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and KitesOBJ: 10-2.1 To find the area of a trapezoid, rhombus, or kite NAT: CC G.MG.1TOP: 10-2 Problem 4 Finding the Area of a Rhombus KEY: area | rhombus

33. ANS: C

PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 3 Identifying and Using the Incenter of a TriangleKEY: angle bisector | incenter of the triangle | point of concurrency

34. ANS: 2.5 cm

PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: 10-6.2 To find the circumference and arc length NAT: CC G.CO.1| CC G.C.1| CC G.C.2| CC G.C.5 TOP: 10-6 Problem 3 Finding a DistanceKEY: circumference | diameter

35. ANS: 3.7 in.

PTS: 1 DIF: L4 REF: 10-3 Areas of Regular PolygonsOBJ: 10-3.1 To find the area of a regular polygon NAT: CC G.CO.13 | CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-3 Problem 2 Finding the Area of a Regular Polygon KEY: regular polygon | hexagon | area | apothem | radius

36. ANS: BG 6, GE 12

PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 5-4.1 To identify properties of medians and altitudes of a triangle NAT: CC G.CO.10| G.3.c TOP: 5-4 Problem 1 Finding the Length of a MedianKEY: centroid of a triangle | median of a triangle

37. ANS:

374.1 yd2

PTS: 1 DIF: L3 REF: 10-5 Trigonometry and AreaOBJ: 10-5.1 To find areas of regular polygons and triangles using trigonometryNAT: CC G.SRT.9| M.1.f TOP: 10-5 Problem 1 Finding AreaKEY: area of a regular polygon | area | regular polygon | tangent | measure of central angle of a regular polygon

ID: A

7

38. ANS: 19 m

PTS: 1 DIF: L2 REF: 11-3 Surface Areas of Pyramids and ConesOBJ: 11-3.1 To find the surface area of a pyramid and a cone NAT: CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-3 Problem 4 Finding the Lateral Area of a Cone KEY: cone | slant height of a cone | Pythagorean Theorem

39. ANS: B PTS: 1 DIF: L4 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumcenter of the triangle | perpendicular bisector | reasoning | right triangle

40. ANS: 7.9

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.hTOP: 12-1 Problem 3 Finding a Radius KEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem

41. ANS: x = 24.0, y = 46.4

PTS: 1 DIF: L3 REF: 8-2 Special Right TrianglesOBJ: 8-2.1 To use the properties of 45-45-90 and 30-60-90 triangles NAT: CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One SideKEY: special right triangles | leg | hypotenuse

42. ANS: 27

PTS: 1 DIF: L4 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c TOP: 5-1 Problem 2 Finding LengthsKEY: midsegment | Triangle Midsegment Theorem

43. ANS: 6

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c TOP: 5-1 Problem 2 Finding LengthsKEY: midpoint | midsegment | Triangle Midsegment Theorem

44. ANS: obtuse

PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.1 To use the Pythagorean theorem and its converse NAT: CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.dTOP: 8-1 Problem 5 Classifying a Triangle KEY: right triangle | obtuse triangle | acute triangle

ID: A

8

45. ANS:

2 5 m

PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.1 To use the Pythagorean theorem and its converse NAT: CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.dTOP: 8-1 Problem 1 Finding the Length of the Hypotenuse KEY: Pythagorean Theorem | leg | hypotenuse

46. ANS: 4

PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectorsNAT: CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Angle Bisector Theorem | angle bisector

47. ANS: 76

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 To use properties of a tangent to a circle NAT: CC G.C.2| G.3.hTOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | angle measure | properties of tangents | central angle

48. ANS: 8

PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.1 To use the Pythagorean theorem and its converse NAT: CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.dTOP: 8-1 Problem 2 Finding the Length of a Leg KEY: Pythagorean Theorem | leg | hypotenuse | Pythagorean triple

49. ANS: 32

PTS: 1 DIF: L3 REF: 10-1 Areas of Parallelograms and TrianglesOBJ: 10-1.1 To find the area of parallelograms and triangles NAT: CC G.GPE.7| CC G.MG.1| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e TOP: 10-1 Problem 2 Finding a Missing Dimension KEY: parallelogram | area | base | height

50. ANS: 292.4 m

PTS: 1 DIF: L3 REF: 8-4 Angles of Elevation and DepressionOBJ: 8-4.1 To use angles of elevation and depression to solve problems NAT: CC G.SRT.8 TOP: 8-4 Problem 3 Using the Angle of DepressionKEY: sine | angles of elevation and depression

ID: A

9

51. ANS:

152 cm2

PTS: 1 DIF: L3 REF: 11-2 Surface Areas of Prisms and CylindersOBJ: 11-2.1 To find the surface area of a prism and a cylinder NAT: CC G.MG.1| N.3.c| N.3.f| N.5.e| M.1.h| A.4.f TOP: 11-2 Problem 3 Finding Surface Area of a Cylinder KEY: surface area of a cylinder | cylinder | surface area formulas | surface area

52. ANS: A PTS: 1 DIF: L2 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c TOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumcenter of the triangle | circumscribe | point of concurrency

53. ANS: A PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 5-6.1 To use inequalities involving angles and sides of triangles NAT: CC G.CO.10| G.3.c TOP: 5-6 Problem 2 Using Theorem 5-10