Name: ______________________ Class: _________________ Date: _________ ID: A

1

GEOMETRY FINAL EXAM REVIEW- Semester 2

1. In the diagram, RS is tangent to Q at R, ST is tangent to Q at T, RS = 117, and ST = 8x + 45. Find the value of x.

2. A castle guard is standing on the opposite side of a 9-foot moat and wants to reach a window that is 26 feet above the ground. The guard props a ladder against the castle wall to form a right triangle as shown. Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot.

ID: A

2

3. Show that quadrilateral DEFG, with vertices D 3,3ÊËÁÁ

ˆ¯̃̃, E 4,0Ê

ËÁÁˆ¯̃̃, F −4,1Ê

ËÁÁˆ¯̃̃, and G −5,4Ê

ËÁÁˆ¯̃̃, is a parallelogram.

ID: A

3

Match the statement below with the diagram it describes. Use each diagram only once.

a. d.

b. e.

c.

4. mAB = 80°

5. mACB = 310°

6. mACB = 180°

7. AB ≅ CD

8. The measure of a central angle is 95°.

9. A physics experiment is set up using two pulleys, a string, and a weight as shown below. The larger pulley has a radius of 12 centimeters, and the smaller pulley has a radius of 5 centimeters. The distance between the centers of the pulleys is 40 centimeters. The string is pulled tightly across both pulleys so that AB is a common tangent of the pulleys. Find the length of string from A to B to the nearest tenth of a centimeter.

ID: A

4

10. The badge shown is shaped like a regular nonagon. Find the measure of each interior angle of the badge. Then find the measure of each exterior angle.

a. interior: 140°; exterior: 40°b. interior: 160°; exterior: 20°c. interior: 40°; exterior: 140°d. interior: 20°; exterior: 160°

11. Find CD.

12. Select the valid similarity statement(s).

a. WEN ∼ WACb. NAJ ∼ CEJc. NEA ∼ CAEd. EWN ∼ WAC

13. The cross section of a brilliant cut diamond is shown. Find the measures of ∠A and ∠D.

ID: A

5

14. In the diagram, YBV ∼ DQA. Find the value of x.

15. Convert 71π180

radians into degrees.

16. Find the area of the triangle. Round your answer to the nearest tenth.

17. Find the number of sides a regular polygon must have so each interior angle measure equals each exterior angle measure. Justify your answer.

18. A parallelogram is formed by the supports that attach a basketball backboard and rim to the wall. The angles change as the basketball apparatus is taken out and put away. Find m∠ADC when m∠DAB = 52°.

ID: A

6

Match the value of x below with one of the diagrams. Use each diagram only once.

a. c.

b. d.

(points B and D are points of tangency)

19. x = 28

20. x = 20

21. x = 65

22. x = 14

Find the volume of the pyramid.

23.

24. Find the sum of the measures of the interior angles of the given figure.

ID: A

7

25. In the diagram, BC = 30 3 . Find AB and AC . Write your answers in simplest form.

26. A Ferris wheel is 470 feet in diameter. How far will a person riding on the Ferris wheel have traveled (in miles) when the wheel makes 43 revolutions? (1 mi = 5280 ft)

27. Find the value of x that makes the quadrilateral a parallelogram when AE = 2x + 3 and CE = 4x − 15.

28. In the diagram, AC = 12 2 . Find AB. Write your answer in simplest form.

29. Write the standard equation of the circle shown below.

ID: A

8

30. A snowball has a diameter of 9 centimeters. What is the volume?

State which theorem you can use to show that the quadrilateral is a parallelogram.

31.

a. Parallelogram Opposite Angles Converseb. Opposite Sides Parallel and Congruent

Theoremc. Parallelogram Opposite Sides Conversed. Parallelogram Diagonals Converse

32.

a. Parallelogram Opposite Angles Converseb. Parallelogram Diagonals Conversec. Opposite Sides Parallel and Congruent

Theoremd. Parallelogram Opposite Sides Converse

33.

a. Parallelogram Opposite Angles Converseb. Parallelogram Opposite Sides Conversec. Opposite Sides Parallel and Congruent

Theoremd. Parallelogram Diagonals Converse

34. Convert 210° to radians.

ID: A

9

35. Decide whether quadrilateral ABCD with vertices A 2,−1ÊËÁÁ

ˆ¯̃̃, B 1,2Ê

ËÁÁˆ¯̃̃, C 4,3Ê

ËÁÁˆ¯̃̃, and D 5,0Ê

ËÁÁˆ¯̃̃ is a

rectangle, rhombus, square, or parallelogram.

a. parallelogramb. rectanglec. squared. rhombus

36. Find the area of the kite.

37. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 22°. When the parasailer is 180 feet above the boat, how long is the rope? Round your answer to the nearest tenth of a foot.

Classify the special quadrilateral.

38.

a. squareb. rectanglec. rhombus

39. The sum of the measures of the interior angles of a polygon is 1800°. Classify the polygon by the number of sides.

40. Find the value of x.

ID: A

10

Solve the triangle. Round decimal answers to the nearest tenth.

41.

42. Two trees are growing in a clearing. The first tree is 16 feet tall and casts a 8 foot shadow. The second tree casts a 18 foot shadow. How tall is the second tree to the nearest tenth of a foot?

43. The end of a charger that is plugged into a phone is an isosceles trapezoid. Find m∠J, m∠K, and m∠M when m∠N = 139°.

44. Find the value of x.

a. 106b. 70c. 76d. 74

Find the exact value of the variable.

45.

46. Determine whether segments with lengths of 30, 19, and 14 form a triangle. If so, classify the triangle as acute, right, or obtuse.

ID: A

11

47. Find the coordinates of the intersection of the diagonals of DEFG with vertices D 4,5Ê

ËÁÁˆ¯̃̃,

E 5,2ÊËÁÁ

ˆ¯̃̃, F 1,3Ê

ËÁÁˆ¯̃̃, and G 0,6Ê

ËÁÁˆ¯̃̃.

48. What is the length of BG?

ID: A

1

GEOMETRY FINAL EXAM REVIEW- Semester 2Answer Section

1. ANS: x = 9

2. ANS: about 27.5 ft

3. ANS: Sample answer: The midpoint of both DF and EG is −0.5,2Ê

ËÁÁˆ¯̃̃. So the diagonals bisect each other and

quadrilateral DEFG is a parallelogram by the Parallelogram Diagonals Converse.4. ANS: B5. ANS: D6. ANS: A7. ANS: C8. ANS: E9. ANS:

39.4 cm10. ANS: A11. ANS:

4312. ANS: A, B13. ANS:

m∠A = 145°,m∠D = 98°

14. ANS: 36

15. ANS: 71°

16. ANS: about 62.0 units2

17. ANS:

4 sides; n − 2( )180°n

= 360°n

n − 2( )180 = 360

180n − 360 = 360

n = 418. ANS:

128°19. ANS: B20. ANS: A21. ANS: C22. ANS: D23. ANS:

27 cm 3

ID: A

2

24. ANS: 360°

25. ANS: AB = 60 3 , AC = 90

26. ANS: about 12.02 mi

27. ANS: x = 9

28. ANS: AB = 24

29. ANS: x − 3( ) 2 + y + 5Ê

ËÁÁˆ¯̃̃

2= 16

30. ANS: about 381.7 cm 3

31. ANS: C32. ANS: C33. ANS: C34. ANS:

7π6

rad

35. ANS: A, B, C, D36. ANS:

75 cm 2

37. ANS: about 480.5 ft

38. ANS: B39. ANS:

dodecagon40. ANS:

about 24.641. ANS:

m∠H = 50°, y ≈ 23.8, c ≈ 31.142. ANS:

36 ft43. ANS:

m∠M = 139°, m∠K = 41°, and m∠J = 41°44. ANS: A45. ANS:

y = 1846. ANS:

obtuse triangle47. ANS:

2.5,4ÊËÁÁ

ˆ¯̃̃

48. ANS: 24

Name: ______________________ Class: _________________ Date: _________ ID: B

1

GEOMETRY FINAL EXAM REVIEW- Semester 2

1. Find the area of the triangle. Round your answer to the nearest tenth.

2. In the diagram, RS is tangent to Q at R, ST is tangent to Q at T, RS = 117, and ST = 8x + 45. Find the value of x.

3. Convert 210° to radians.

ID: B

2

Match the statement below with the diagram it describes. Use each diagram only once.

a. d.

b. e.

c.

4. mACB = 180°

5. mACB = 310°

6. AB ≅ CD

7. mAB = 80°

8. The measure of a central angle is 95°.

9. Two trees are growing in a clearing. The first tree is 16 feet tall and casts a 8 foot shadow. The second tree casts a 18 foot shadow. How tall is the second tree to the nearest tenth of a foot?

10. What is the length of BG?

ID: B

3

Classify the special quadrilateral.

11.

a. squareb. rectanglec. rhombus

12. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 22°. When the parasailer is 180 feet above the boat, how long is the rope? Round your answer to the nearest tenth of a foot.

State which theorem you can use to show that the quadrilateral is a parallelogram.

13.

a. Parallelogram Opposite Sides Converseb. Opposite Sides Parallel and Congruent

Theoremc. Parallelogram Diagonals Conversed. Parallelogram Opposite Angles Converse

14.

a. Parallelogram Opposite Sides Converseb. Opposite Sides Parallel and Congruent

Theoremc. Parallelogram Opposite Angles Conversed. Parallelogram Diagonals Converse

15.

a. Parallelogram Diagonals Converseb. Parallelogram Opposite Sides Conversec. Opposite Sides Parallel and Congruent

Theoremd. Parallelogram Opposite Angles Converse

16. Convert 71π180

radians into degrees.

ID: B

4

17. In the diagram, YBV ∼ DQA. Find the value of x.

18. The badge shown is shaped like a regular nonagon. Find the measure of each interior angle of the badge. Then find the measure of each exterior angle.

a. interior: 140°; exterior: 40°b. interior: 40°; exterior: 140°c. interior: 160°; exterior: 20°d. interior: 20°; exterior: 160°

19. A snowball has a diameter of 9 centimeters. What is the volume?

20. Find the value of x.

a. 70b. 74c. 76d. 106

ID: B

5

21. A physics experiment is set up using two pulleys, a string, and a weight as shown below. The larger pulley has a radius of 12 centimeters, and the smaller pulley has a radius of 5 centimeters. The distance between the centers of the pulleys is 40 centimeters. The string is pulled tightly across both pulleys so that AB is a common tangent of the pulleys. Find the length of string from A to B to the nearest tenth of a centimeter.

Match the value of x below with one of the diagrams. Use each diagram only once.

a. c.

b. d.

(points B and D are points of tangency)

22. x = 28

23. x = 65

24. x = 14

25. x = 20

26. Find the number of sides a regular polygon must have so each interior angle measure equals each exterior angle measure. Justify your answer.

ID: B

6

27. The end of a charger that is plugged into a phone is an isosceles trapezoid. Find m∠J, m∠K, and m∠M when m∠N = 139°.

28. The cross section of a brilliant cut diamond is shown. Find the measures of ∠A and ∠D.

29. The sum of the measures of the interior angles of a polygon is 1800°. Classify the polygon by the number of sides.

Find the volume of the pyramid.

30.

31. Write the standard equation of the circle shown below.

ID: B

7

32. In the diagram, BC = 30 3 . Find AB and AC . Write your answers in simplest form.

33. A castle guard is standing on the opposite side of a 9-foot moat and wants to reach a window that is 26 feet above the ground. The guard props a ladder against the castle wall to form a right triangle as shown. Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot.

ID: B

8

34. Decide whether quadrilateral ABCD with vertices A 2,−1ÊËÁÁ

ˆ¯̃̃, B 1,2Ê

ËÁÁˆ¯̃̃, C 4,3Ê

ËÁÁˆ¯̃̃, and D 5,0Ê

ËÁÁˆ¯̃̃ is a

rectangle, rhombus, square, or parallelogram.

a. parallelogramb. rhombusc. squared. rectangle

35. Find the sum of the measures of the interior angles of the given figure.

36. Find the coordinates of the intersection of the diagonals of DEFG with vertices D 4,5Ê

ËÁÁˆ¯̃̃,

E 5,2ÊËÁÁ

ˆ¯̃̃, F 1,3Ê

ËÁÁˆ¯̃̃, and G 0,6Ê

ËÁÁˆ¯̃̃.

37. A Ferris wheel is 470 feet in diameter. How far will a person riding on the Ferris wheel have traveled (in miles) when the wheel makes 43 revolutions? (1 mi = 5280 ft)

38. In the diagram, AC = 12 2 . Find AB. Write your answer in simplest form.

ID: B

9

39. Show that quadrilateral DEFG, with vertices D 3,3ÊËÁÁ

ˆ¯̃̃, E 4,0Ê

ËÁÁˆ¯̃̃, F −4,1Ê

ËÁÁˆ¯̃̃, and G −5,4Ê

ËÁÁˆ¯̃̃, is a

parallelogram.

40. Find the value of x.

41. A parallelogram is formed by the supports that attach a basketball backboard and rim to the wall. The angles change as the basketball apparatus is taken out and put away. Find m∠ADC when m∠DAB = 52°.

42. Find CD.

ID: B

10

43. Find the value of x that makes the quadrilateral a parallelogram when AE = 2x + 3 and CE = 4x − 15.

44. Find the area of the kite.

Solve the triangle. Round decimal answers to the nearest tenth.

45.

46. Select the valid similarity statement(s).

a. NAJ ∼ CEJb. EWN ∼ WACc. WEN ∼ WACd. NEA ∼ CAE

ID: B

11

Find the exact value of the variable.

47.

48. Determine whether segments with lengths of 30, 19, and 14 form a triangle. If so, classify the triangle as acute, right, or obtuse.

ID: B

1

GEOMETRY FINAL EXAM REVIEW- Semester 2Answer Section

1. ANS: about 62.0 units2

2. ANS: x = 9

3. ANS: 7π6

rad

4. ANS: A5. ANS: D6. ANS: C7. ANS: B8. ANS: E9. ANS:

36 ft10. ANS:

2411. ANS: B12. ANS:

about 480.5 ft13. ANS: B14. ANS: A15. ANS: C16. ANS:

71°17. ANS:

3618. ANS: A19. ANS:

about 381.7 cm 3

20. ANS: D21. ANS:

39.4 cm22. ANS: B23. ANS: C24. ANS: D

ID: B

2

25. ANS: A26. ANS:

4 sides; n − 2( )180°n

= 360°n

n − 2( )180 = 360

180n − 360 = 360

n = 427. ANS:

m∠M = 139°, m∠K = 41°, and m∠J = 41°28. ANS:

m∠A = 145°,m∠D = 98°

29. ANS: dodecagon

30. ANS: 27 cm 3

31. ANS: x − 3( ) 2 + y + 5Ê

ËÁÁˆ¯̃̃

2= 16

32. ANS: AB = 60 3 , AC = 90

33. ANS: about 27.5 ft

34. ANS: A, B, C, D35. ANS:

360°36. ANS:

2.5,4ÊËÁÁ

ˆ¯̃̃

37. ANS: about 12.02 mi

38. ANS: AB = 24

39. ANS: Sample answer: The midpoint of both DF and EG is −0.5,2Ê

ËÁÁˆ¯̃̃. So the diagonals bisect each other and

quadrilateral DEFG is a parallelogram by the Parallelogram Diagonals Converse.40. ANS:

about 24.641. ANS:

128°42. ANS:

4343. ANS:

x = 944. ANS:

75 cm 2

ID: B

3

45. ANS: m∠H = 50°, y ≈ 23.8, c ≈ 31.1

46. ANS: A, C47. ANS:

y = 1848. ANS:

obtuse triangle