Geometry 2-B



Geometry Final Exam Review – Ch. 7 Name:_________________________________

Hour: ____

SIMPLIFY each ratio completely.

1. [pic] = 2. [pic] = 3. [pic] = 4. 32 : 4 = 5. 30 : 39 =

Convert units to simplify each ratio.

6. [pic] = 7. [pic] = 8. [pic] = 9. [pic] = 10. [pic] =

|A basketball team won 12 games and lost 8. Reduce each ratio. |15. In the diagram, JK : KL is 7 : 2 and JL =36. |

|11. wins to losses |Find JK and KL. |

| |Equation: |

|12. wins to the total number of games played | |

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|13. losses to wins | |

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|14. losses to the total number of games played | |

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| |x = _____ JK = _____ KL = ______ |

|16. Use the triangles to write each ratio in simplest form. |17. Use the triangles to write each ratio in simplest form. |

|[pic] ________ |[pic] = _______ [pic] = _______ |

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|[pic] ________ |[pic] = _______ [pic] = _______ |

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|[pic] ________ |[pic] = _______ [pic] = _______ |

Solve these proportions by cross-multiplying. Use the distributive property where needed. Show your work!

18. [pic] 19. 8 : 3 = x : 6 20. [pic] 21. [pic]

Proportion:

Set up a PROPORTION to solve the following problems.

|22. If 25 Valentine chocolate candies cost $20.00. |23. Thomas finished 50 math problems in 20 minutes. At this rate, how many math |

|How much will 42 Valentine chocolates cost? |problems can he do in 30 minutes? |

|Proportion: |Proportion: |

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|Answer = __________ |Answer = __________ |

24. Shapes that are SIMILAR are the same shape, but not necessarily the same _____________.

25. In SIMILAR shapes, the corresponding angles are _____________and the corresponding sides are _____________________.

The two polygons are similar. Write a proportion and solve for x.

26. 27. 28.

Proportion to find x and solve: Proportion to find x and solve: Proportion to find x and solve:

|29. |30. |31. |

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|[pic]Scale Factor: _______ |[pic]Scale Factor: ________ |[pic]Scale Factor: _______ Proportion to find x: |

|Proportion to find x: Proportion to find y: |Proportion to find x: Proportion to find y: |Proportion to find y: |

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|32. The two rectangles are similar. |33. The scale factor of two similar triangles is 4 |

|a. Find the scale factor (left to right). |: 7, find the ratio of the perimeters. |

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|b. Find the ratio of the perimeters of the rectangles. | |

Determine if the triangles are similar by AA~, SSS~, SAS~, or none. Work must be shown to check proportions and/or angles!

34. 35. 36.

Check Proportions and/or Angles: Check Proportions and/or Angles: Check Proportions and/or Angles:

Postulate: _________ Postulate: _________ Postulate: _________

37. 38. 39.

Check Proportions and/or Angles: Check Proportions and/or Angles: Check Proportions and/or Angles:

Postulate: _________ Postulate: _________ Postulate: _________

Find the missing angles and set up proportions to find the missing side lengths for the similar triangles.

40. 41.

Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y:

m(T= ______ m(N = ______ m(D = ______ m(T = ______ m(A = ______

42. 43.

"Flipped" or "Twisted" Bow Tie? "Flipped" or "Twisted" Bow Tie?

[pic] [pic]

Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y:

m(P = ______ m(ATC = ______m(A = ______ m(1 = ______ m(A = ______ m(E = ______

44. Separate and label triangles here: 45. Separate and label triangles here:

[pic]Scale Factor: ________ [pic]Scale Factor: ________

Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y:

m(E = ______ m(D= ______ m(F = ______ m(D = ______ m(BCA = ______m(A = ______

Complete the following proportions by using the picture at the right.

46. [pic] ? = _______ 47. [pic] ? = _______

48. [pic] ? = _______ 49. [pic] ? = _______

Use a proportion to solve for the missing length.

49. 50. 51. 52.

Proportion to find x: Proportion to find x: Proportion to find z: Proportion to find x:

Separate the picture into two labeled triangles and find the missing information.

53. Separate the picture into two labeled triangles. 54. Separate the picture into two labeled triangles

Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y.

Use the MIDSEGMENT FORMULA to solve for the length of the variable.

55. 56. 57. 58.

x = ________ a = ________ b = ________ y = ________

Geometry Final Exam Review – Ch. 8 Name:_________________________________

Hour: ____

1. How do you find the perimeter of any shape?__________________________

Find the perimeter of each shape.

2. 3. 4. 5.

6-7. Draw a rectangle with the following dimensions.

6. Draw a rectangle with perimeter 12 7. Draw a rectangle with perimeter 10

and area 8. and area 4.

Converting units. Fill in the blanks.

8. 1 yd = _____ feet 9. 2 yd = _____ feet 10. 6 feet = ____ yards 11. 12 feet = ____yards

12. 1 foot = ___ inches 13. 5 feet = ___inches 14. 24 inches = ___feet 15. 48 inches = ____ft

16. 1 meter = ____cm 17. 4 meters = ____cm 18. 5 cm = ____mm 19. 12 cm = ______mm

20. How do you find the area of a rectangle?_________________

21. How do you find the area of a parallelogram?_______________

Find the area of each rectangle or parallelogram.

22. 23. 24. 25.

26. 27. 28. 29.

Given the dimensions of a parallelogram, find the area.

30. base = 24 cm 31. base = 18 in 32. base = 16.2 m 33. base = 45 ft

height = 5 cm height = 25 in height = 9.4 m height = 8 yd

Find x for each parallelogram.

34. Area = 48 cm2 35. Area = 63 in2

36. How do you find the area of a triangle?_____________________

Find the area of each triangle.

37. 38. 39. 40.

Find x for each triangle.

41. Area = 32 in2 42. Area = 24 in2

Fill in the following formulas.

43. Area of a trapezoid _____________________ 44. Area of a rhombus __________________________

45. Area of a regular polygon ________________

Find the area of each shape.

46. A trapezoid with bases of length 10in and 12 in, and height 7 in.

47. A rhombus with diagonals of length 14in and 6 in.

48. A regular octagon with sides of length 8 mm and apothem of 9.7 mm.

49. A regular pentagon with sides length 20 cm and apothem 13.7 cm.

Find the area of the shaded region.

Find the area of the shaded region.

[pic]

Area rectangle=_______ Area rectangle=_______ Area parallelogram=_______ Area parallelogram=_______

Area triangle=_______ Area triangle=_______ Area rectangle=_______ Area square=_______

Shaded area=_______ Shaded area=_______ Shaded area=_______ Shaded area=_______

Match the name of each polygon with the number of sides.

57. Octagon_____ 61. Nonagon _____ A. 3 sides E. 7 sides

58. Hexagon _____ 62. Pentagon _____ B. 4 sides F. 8 sides

59. Heptagon _____ 63. Decagon _____ C. 5 sides G. 9 sides

60. Quadrilateral _____ 64. Triangle _____ D. 6 sides H. 10 sides

Classify (Name) the polygon by its number of sides.

65. 66. 67. 68. 69.

70. How many DIAGONALS from point X does each polygon have?

71. A REGULAR POLYGON has all equal ____________ and all equal __________ Draw and label a regular polygon with… 3 sides 4 sides 5 sides 6 sides 8 sides

72. Fill in the chart.

|Name |Picture |# of Sides |SUM of Interior ∠’s |EACH interior Angle |SUM of Exterior ∠’s |EACH Exterior Angle |

|Triangle | | | | | | |

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|Quadrilateral | | | | | | |

| | | | | | | |

|Pentagon | | | | | | |

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|Hexagon | | | | | | |

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|FORMULAS |No picture |n | | | | |

|Memorize them! | | | | | | |

For each regular polygon, find the SUM of the interior angles and the measure of EACH interior angle.

73. Octagon (8 sides) 74. Polygon with 15 sides 75. Polygon with 20 sides

SUM of Interior Angles ____________ SUM of Interior Angles ____________ SUM of Interior Angles ____________

EACH interior angle ____________ EACH interior angle ____________ EACH interior angle ____________

Find the measure of the missing angle.

76. 77. 78. 79.

# of sides___ Sum of Interior ∠’s _____ # of sides___ Sum of Interior ∠’s ____ # of sides___ Sum of Interior ∠’s ____ # of sides___ Sum of Interior ∠’s ____

m∠D =_______ m∠A =_______ m∠D =_______ m∠A =_______

Given the SUM of the INTERIOR angles, work backwards to find the number of SIDES in each shape.

80. 720° 81. 1080° 82. 1620° 83. 2880°

For each regular polygon, find the SUM of exterior angles and the measure of EACH exterior angle.

84. Octagon (8 sides) 85. Polygon with 15 sides 86. Polygon with 20 sides

SUM of Exterior Angles ____________ SUM of Exterior Angles ____________ SUM of Exterior Angles ____________

EACH Exterior angle ____________ EACH Exterior angle ____________ EACH Exterior angle ____________

Write an equation and solve for x.

87. 88. 89. 90.

SUM of Exterior Angles ____________ SUM of Exterior Angles ____________ SUM of Exterior Angles ____________ SUM of Exterior Angles ____________

Equation: Equation: Equation: Equation:

Given the measure of EACH EXTERIOR angle in a regular polygon, work backwards to find the number of SIDES.

91. 12° 92. 120° 93. 90° 94. 45°

Classify each figure as CONVEX (“caved out”) polygon, CONCAVE (“caved in”) polygon or Not a Polygon.

95. 96. 97. 98.

Ch. 8 CIRCLE Final Exam Review

MATCH the key word with the descriptive phrase.

____1. The set of all point in a plane that are the same distance from a given point

____2. The distance from the center to a point on the circle

____ 3. The distance across the circle, through the center

____4. The distance around a circle

____ 5. The amount of surface covered by a circle

____6. A portion of the AREA of a circle

____7. A portion of the CIRCUMFERENCE of a circle

8. What is the relationship between the radius and the diameter?_______________

9. If the radius is 7 cm, then the diameter is _______ If the diameter is 18 m, then the radius is __________

10. State the FORMULA for CIRCUMFERENCE of a circle: ________________

EXACT: use the  symbol – NOT 3.14 APPROX: use 3.14 – NOT the  symbol or the  key

Find the exact and approximate CIRCUMFERENCE of each circle. Your answers should have plain units.

11. 12. 13. Diameter = 20 mm 14. Radius = 4 cm

EXACT circumference __________ EXACT circumference __________ EXACT circumference __________ EXACT circumference __________

APPROX circumference __________ APPROX circumference __________ APPROX circumference __________ APPROX circumference __________

|15. A farmer wants to build a circular pen for his chicken. He wants the radius |16. A bicycle tire has a diameter of 24 inches. How far does the tire go in ONE |

|of his pen to be 25 ft. Approximately how many feet of fencing would he need to |revolution? |

|build the pen? |(Hint: use circumference formula) |

|Which formula will you use for fencing? Circumference or Area? | |

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| |How far does the tire go in 10 revolutions? |

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Given the CIRCUMFERENCE, work backwards using the formula to find the diameter and radius.

17. Circum= 50 18. Circum = 6 19. Circum = 18.84 20. Circum = 21.98

d = ________ r = _________ d = ________ r = _________ d = ________ r = _________ d = ________ r = _________

21. State the FORMULA for finding ARC LENGTH: ___________________

Use the formula above to find the arc length of AB.

22. 23. 24. 25.

26. State the FORMULA for AREA of a circle: ________________

EXACT: use the  symbol – NOT 3.14 APPROX: use 3.14 – NOT the  symbol or the  key

Find the exact and approximate AREA of each circle. Your answers should have square units.

27. 28. 29. Radius = 3 m 30. Diameter = 8 in.

EXACT area __________ EXACT area __________ EXACT area __________ EXACT area __________

APPROX area __________ APPROX area __________ APPROX area __________ APPROX area __________

Given the AREA, work backwards using the formula to find the radius.

31. Area = 36 cm2 32. Area = 64 m2 33. Area = 78.5 ft2 34. Area = 12.56 cm2

35. State the FORMULA for finding the AREA OF A SECTOR: _____________________

Find the area of each sector.

36. 37. 38. 39.

Find the area of the shaded region.

40. 41. 42. 43.

Exact area of big circle:_________ Exact area of square:_________ Exact area of rectangle:________ Exact area of parallelogram:_____

Exact area of small circle:_______ Exact area of circle:_______ Exact area of circle:_______ Exact area of circle:_______

Area of Shaded region: _________ Area of Shaded region: ______ Area of Shaded region: _______ Area of Shaded region: _________

A pizza is cut into 8 congruent pieces as shown. The diameter of the pizza is 16 inches.

44. Find the circumference of the pizza.

46. Find the radius of the pizza.

47. Find the area of the top of the entire pizza.

Geometry Final Exam Review – Ch. 9 Name:_________________________________

Hour: ____

Tell whether the solid is a polyhedron. If so, name the solid.

1. 2. 3. 4.

Name the polyhedron. Then count the number of faces and edges.

5. 6. 7.

Name: Name: Name:

Faces: Faces: Faces:

Edges: Edges: Edges:

Use Euler’s formula F + V = E + 2 to find the number of faces, edges or vertices.

8. A prism has 4 faces and 6 edges. How many vertices does it have?

9. A pyramid has 5 faces and 6 vertices. How many edges does it have?

10. A pyramid has 12 edges and 7 vertices. How many faces does it have?

Name the solid, then find the surface area to the nearest whole number.

11. 12. 13.

Name: Name: Name:

14. 15. 16.

Name: Name: Name:

17. 18. 19.

Name: Name: Name:

20. 21. 22.

Name: Name: Name:

Name the solid. Then find the volume of the solid.

23. 24. 25.

Name: Name: Name:

26. 27. 28.

Name: Name: Name:

29. 30. 31.

Name: Name: Name:

32. 33. 34.

Name: Name: Name:

Geometry Final Exam Review – Ch. 10 Name:_________________________________

Hour: ____

Find the value of each expression.

1. [pic] = ____ 2. [pic] = ______ 3. 122 = _______ 4. 82 = _____

List the perfect squares from 1 to 225

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|29. How long is the hypotenuse of a doorway that is 9 feet by 4 feet? |30. A helicopter flies 9 miles due east and then 6 miles due south. How far is if|

| |from its starting point? |

|Equation: | |

| |Equation: |

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|Can a mattress that is 10 feet long fit through the doorway?________ | |

Remind yourself of the 45-45-90 and 30-60-90 triangle rules!

45-45-90: hypotenuse = leg[pic] 30-60-90: hypotenuse = short leg [pic]

|[pic] |[pic] |

Use the special triangle rules to find the missing sides of the following triangles.

31. 32. 33.

x = _______ y = ______ x = _______ y = ______ x = _______ y = ______

34. 35. 36.

x = _______ y = ______ x = _______ y = ______ x = _______ y = ______

37. Us a CALCULATOR set in DEGREE mode to find the following values. Round answers to nearest hundredth.

a) Sin 45 = ________ b) tan 30 = _______ c) cos 90 = ______ d) cos 60 = ______ e) sin 60 = ________

Fill in the ratios for each trig function using the words: opposite, adjacent and hypotenuse.

How do we remember these definitions? _________________________________________

For each triangle, give the sin, cos, and tan in fraction form. Find the missing sides where needed and reduce all fractions!

38. 39. 40.

a = ____

Use sin, cos, or tan proportion to solve for the variable.

41. 42. 43.

a = ________ a = ________ a = ________

|44. Donovan leans a 15-ft ladder against the wall. The ladder makes a 70° angle |45. A tree casts a shadow 25 feet long when the angle of elevation to the sun is |

|with the ground. How far up the building does the ladder reach? |68°. How tall is the tree? |

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Use SOH CAH TOA to find the missing ANGLE. Write an equation and use the INVERSE to find the angle measure. Round to nearest 100th of a degree.

46. 47.

m∠A = ____________ m∠A = ___________

|48. Stefan leans a 20-ft ladder against a wall. The base of the ladder is 3 feet|49. Chelsea visited the Washington Monument which is 550ft tall on her summer |

|from the wall. What ANGLE does the ladder make with the ground? |vacation. She stood 400 feet away from the base of the monument to take a |

| |picture. At what ANGLE did she need look up to ensure that she captured the top |

| |of the monument in her picture? |

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Geometry Final Exam Review – Ch. 11 Name: ________________________

Hour: _____

1. How many degrees are in a circle?___________ 2. How many degrees are in a semicircle? _____________

Name each of the following for circle O.

3. A semicircle __________

4. Two minor arcs __________ and __________

5. Two major arcs__________ and __________

6. In a circle, the measure of the central angle is the ____________ the measure of the arc.

Find the measure of each angle for each arc of circle P.

7. m∠SPR______________ 8. [pic] ________________

9. [pic] ________________ 10. [pic] ________________

11 . [pic] ________________ 12. [pic] ________________

13. In a circle, the measure of the inscribed angle is the _____________ the measure of the arc.

14. What is the measure of an angle that is inscribed in a semicircle?________________

Find the measure of the following angles and arcs.

15. 16. 17.

18. What is a tangent segment?_________________

19. What kind of angle is formed when a radius and a tangent meet? ________________

20. If two tangent segments are drawn from a point outside the circle, these segments are ___________

Find the lengths of the following segments.

21. 22. 23.

SR = _____ OT = ______ MT = _________ OC = ____ OB = _____ AB = ____

24. Equal chords mean _________ arcs. 25. If a diameter is perpendicular to a chord, then it_______

the chord and the arc.

Using the given picture, find the following lengths.

Note: PD = 5, BE = 2

26. PB = _____________ 27. PC = ______________

28. PE = _____________ 29. CE = ______________

30. AE = ____________

Draw the following.

31. a triangle inscribed in a square 32. A circle inscribed in a triangle 33. A triangle circumscribed about a circle

What is the rule for finding the angle in a picture that is Chord-Chord ____________________________

Find the following angles.

34. m∠1=___________ 35. m∠1=_______ m∠2=_________ 36. m∠1=_______ m∠2=_________

What is the rule for finding the angle in a picture that is tangent-chord _______________________

Find the following angles.

37. m∠1=___________ 38. m[pic]=_______ m∠1=_________ 39. m∠1=_______ m∠2=_________

What is the rule for finding angle 1 in each of the following pictures ___________________

Find the following angles.

40. m∠1=___________ 41. m∠1=_________ 42. m[pic]=_______ m∠1=_________

Write an equation and solve for x.

43. 44. 45.

Equation:________________ Equation:________________ Equation:________________

Answer: _________________ Answer: _________________ Answer: _________________

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51.

36

52.

50.

53.

54. 55. 56. 57.

78.

79.

A. diameter

B. radius

C. circle

D. circumference

E. area

F. arc length

G. area of sector

sin A_____ sin B_______

cos A______ cos B_______

tan A ______ tan B ______

sin A_____ sin B_______

cos A______ cos B_______

tan A ______ tan B ______

sin A_____ sin B_______

cos A______ cos B_______

tan A ______ tan B ______

43.

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