advanced algebra€¦  · web view30-60-90 formulas: sine: cosine: tangent: area of a rectangle:...

GEOMETRY PRACTICE FINAL—MRS. BERGANTZ

Name:___________________________________________ Date:__________________________

Define the following words:

1. collinear:

2. coplanar:

3. bisect:

4. linear pair:

5. complementary:

6. supplementary:

7. perimeter:

8. hypothesis of a conditional:

9. conclusion of a conditional:

10. biconditional:

11. midsegment of a triangle:

12. median of a triangle:

13. perpendicular bisector of a segment:

14. altitude of a triangle:

15. angle bisector:

16. parallelogram:

17. rhombus:

18. rectangle:

19. square:

20. trapezoid:

21. isosceles trapezoid:

22. kite:

State the formulas for the following:

23. distance:

24. midpoint:

25. circumference of a circle:

26. area of a circle:

27. slope between two points:

28. slope-intercept form:

29. point-slope form:

30. midsegment of a triangle:

31. sum of interior angles of a polygon:

32. ONE interior angle of a regular polygon:

33. sum of exterior angles in a polygon

34. ONE exterior angle in a regular polygon:

35. midsegment of a trapezoid:

36. Pythagorean Theorem:

37. 45-45-90 formula:

38. 30-60-90 formulas:

39. Sine:

40. Cosine:

41. Tangent:

42. Area of a rectangle:

43. Area of a parallelogram:

44. Area of a triangle:

45. Area of a trapezoid:

46. Area of a rhombus

47. Area of a kite:

48. Area of a regular polygon:

Give an example of the following properties:

49. Reflexive:

50. Symmetric:

51. Distributive:

52. Transitive:

53. Substitution:

1. For the following figure, make an isometric drawing:

2. For the following, make an orthographic drawing:

3. Draw a net of the following 3D shape:

For the following problems, use the figure to the right.

4. Name the plane parallel to plane GHJK.

5. Name the intersection of plane GHML and plane HMNJ.

6. Name the intersection of and .

7. Name a fourth point in plane HLP.

Use the diagram to the right to answer the following questions.

8. Name plane P another way.

9. Name the intersection of plane P and plane Q.

10. Name a pair of opposite rays in the line below.

11. For the line above, name all segments (without repeating):

12. For the line above, name all rays (without repeating):

13. On the number line below, find BE .

14. If Q is the midpoint of , and PQ = and QR = , find x, PQ, QR, and PR.

ABCVx =____________________

PQ=___________________

QR=___________________

PR=___________________

15. Find the value of x and the measures of all of the angles, given the following information.

16. Find the coordinates of the midpoint of the segment connecting endpoints H and K .

17. The coordinates of point X are . The midpoint of has coordinates . Find the coordinates of point Y.

18. Find the perimeter of the polygon.

19. Find the distance between points P and Q . Round your answer to the nearest tenth.

20. Find the circumference of the circle to the right. Leave your answer in terms of pi.

21. Find the area of the circle to the right. Round your answer to the nearest tenth.

22. Identify the hypothesis and conclusion of the following conditional statement. If it is a dog, then it is a pet.

23. Write the converse, inverse and contrapositive of the following statement. State the truth value for each statement. If any are false, provide a counterexample.

If you live in Missouri, then you live in the United States.

Converse:

Inverse:

Contrapositive:

24. Write the two conditional statements that make up the following biconditional. Two angles have the same measure if and only if the angles are congruent.

1.

2.

25. Write the following as a biconditional statement. A rhombus is a quadrilateral with four congruent sides..

26. Is the following a good definition? Explain. A dog is a good pet.

27. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not possible.

Statement 1: If a figure is a rectangle, then it has two pairs of parallel sides.Statement 2: Figure ABCD is a rectangle.

28. Use the Law of Syllogism to draw a conclusion from the following statements. If not possible, state not possible.

If a number is prime, then it does not have repeated factors.If a number does not have repeated factors, then it is not a perfect square.

29. Use the Law of Detachment to draw a conclusion from the following statements. If not possible, state not possible.

If the river is flooded, then driving on the bridge is dangerous..Driving on the bridge is dangerous.

30. Supplementary angles are two angles whose measures have sum __________.

31. Complementary angles are two angles whose measures have sum__________.

Using the figure below, answer the following questions.

32. Name an angle complementary to .

33. Name a linear pair.

34. Name a pair of supplementary angles.

35. Name a pair of vertical angles.

Name the property of equality that justifies each of the following statements:

36. a ( b + c ) = ab + ac.

37. If a = b, and b = c, then a = c.

38. BC = BC

Use the diagram to the right to answer the questions below.

39. ∠2 and ∠14 are ______________________________________________ angles.

40. ∠1 and ∠3 are ______________________________________________ angles.

41. ∠2 and ∠8 are ______________________________________________ angles.

42. ∠6 and ∠9 are ______________________________________________ angles.

43. Find the value of x for p to be parallel to q.

m∠1 = 95º and m∠6 =

44. Find the value of m.

45. Find the value of x, y, and z in the diagram below.

46. Find the value of a, b, and c in the following triangle.

47. In the following, a, b, c, d and e are distinct lines in the same plane. Sketch the given relationships between each line (draw a picture).State the relationship between line a and line e.

For the following questions, use the figure to the right.

48. Name two lines skew to

49. Name all lines parallel to

50. Name two planes that are parallel

51. Find the slope between the following points (2, -3) and (-4, 1)

52. Write the equation of the line in POINT-SLOPE form that goes through the point (3, –7) and has

slope .

53. Write the equation of the line in POINT-SLOPE form that contains the points S (6, –5) and T (8, –2).

54. Find the slope of the line perpendicular to .

55. Write the equation of the line in POINT-SLOPE form that is parallel to

and contains the point P(–8, 1).

56. Write the equation of the line in POINT-SLOPE form that is perpendicular to through the point P(2, -6).

57. Given that the two triangles below are congruent, find the value of h.

Name the postulate that proves that the following triangles are congruent.

58. 59.

60. 61.

62. What does the abbreviation CPCTC mean?

63. Complete the following proof:

Statements Reasons

64. Complete the following proof:

Statements Reasons

Find the value of the variable.

65. 66.

Use the diagram to identify the following special segments:

67. Name a median:

68. Name a perpendicular bisector:

69. Name an altitude:

70. Name an angle bisector:

71. Find the value of x in the diagram to the right.

72. Find the measure of

73. List the sides in order from longest to shortest.

74. and . Find the angle measures and then list the sides of in order from shortest to longest.

75. ABC, where AB = 17, AC = 13, and BC = 29, list the angles in order from smallest to largest.

76. Can a triangle have sides with the following lengths? Explain. 2 cm, 3 cm, 7 cm.

77. The lengths of two sides of a triangle are given. Describe the lengths possible for a third side.7 ft, 11 ft

78. Find the sum of the measures of the angles of a decagon.

79. Find the measure of an interior angle and an exterior angle of a regular octagon.

One interior angle:

One exterior angle:

80. Find the value of x .

Find the values of the variables in the parallelograms below.

81. 82.

Find the value of the variables in the figures below.

83. 84.

Find the measures of the numbered angles in the figures below.

85. (rectangle) 86.

87. DEFG is a rectangle. and . Find the value of x and the length of each diagonal.

88. Find the slope and distance of each side of the quadrilateral with the following vertices. Classify the quadrilateral. A (-5, 2), B (-3, 6), C(6, 6) and D (4, 2)

89.A model of a car is 3.5 inches long. A similar actual version of the car is 13 ft long. Write a ratio of the size of the model car to the size of the actual car.

90. If , then =________.

Solve each proportion.

91. 92.

93. A map of Australia has a scale of 1cm: 120 km. If the distance between Melbourne and Canberra is 463 km, how far apart are they on the map, to the nearest tenth of a cm?

94. ABCDE ~ GHJDF. Complete the statements.

95. The figures below are similar. Find the value of the variables.

96. The polygons below are similar. Find the values of the variables.

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

97. 98.

The triangles below are similar. Find the value of x.

99. 100.

Find the value of x.

101. 102.

Simplify the following. Leave your answers in simplest radical form.

103. 104.

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

105. 106.

107. A triangle has sides with lengths 12, 14, and 19. Classify the triangle as right, acute, or obtuse.

108. A triangle has side lengths 10cm, 24cm, and 34 cm. Is it a right triangle?

109.Find the length of the hypotenuse. 110. Find the length of the legs. Leave your answer in simplest radical form.

Find the values of the variables. If your answer is not an integer, leave it in simplest radical form.

110. 111.

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

112. 113.

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

114. 115.

Find the area.

116. 117.

Find the area of the trapezoid and the kite below.

118. 119.

Find the area of the following regular polygons:

120.

Find the area of the following regular polygons:

ABCV

121.

Graph each equation:

1. 2.

3. 4.

5. 6.