Name: ________________________ Class: ___________________ Date: __________ ID: A 1 Geometry Final Exam Review 2015 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. What is the value of x if ABC is equilateral? a. -8 c. 1 2 b. - 1 8 d. 2 Use the figure below. ____ 2. What is m∠2? a. 50 c. 110 b. 70 d. 120 ____ 3. What is m∠4? a. 10 c. 100 b. 60 d. 120 ____ 4. What are the congruent triangles in the diagram? a. ABC ≅ EBD c. AEB ≅ CBD b. ABE ≅ CBD d. ABE ≅ CDB
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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Geometry Final Exam Review 2015
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. What is the value of x if ABC is equilateral?
a. −8 c.1
2
b. −1
8d. 2
Use the figure below.
____ 2. What is m∠2?
a. 50 c. 110
b. 70 d. 120
____ 3. What is m∠4?
a. 10 c. 100
b. 60 d. 120
____ 4. What are the congruent triangles in the diagram?
a. ABC ≅ EBD c. AEB ≅ CBD
b. ABE ≅ CBD d. ABE ≅ CDB
Name: ________________________ ID: A
2
____ 5. If CJW ≅ AGS, m∠A = 50, m∠J = 45, and m∠S = 16x + 5, what is x?
a. 17.5 c. 6
b. 11.875 d. 5
____ 6. A triangular-shaped roof of a house has congruent legs. What is the measure of each of the two base angles?
a. 25 c. 100
b. 50 d. 120
____ 7. What is the length of the sides of this equilateral triangle?
a. 42 c. 15
b. 30 d. 12
____ 8. How would ABC with vertices A(4, 1), B(2, −1), and C(−2, −1) be classified based on its sides?
a. equilateral c. scalene
b. isosceles d. right
____ 9. If DJL ≅ EGS, which segment in EGS corresponds to DL ?
a. EG c. GS
b. ES d. GE
____ 10. Which triangles are congruent in the figure?
a. KLJ ≅ MNL c. JKL ≅ LMN
b. JLK ≅ NLM d. JKL ≅ MNL
Name: ________________________ ID: A
3
____ 11. If ABC is isosceles and AE ≅ FC, which theorem or postulate can be used to prove AEB ≅ CFB?
a. SSS c. ASA
b. SAS d. AAS
____ 12. Find the sum of the measures of the interior angles of a convex 30-gon.
a. 5400 c. 360
b. 5040 d. 168
____ 13. Find the sum of the measures of the exterior angles of a convex 21-gon.
a. 21 c. 360
b. 180 d. 3420
____ 14. If the measure of each interior angle of a regular polygon is 108, find the measure of each exterior angle.
a. 18 c. 90
b. 72 d. 108
____ 15. For parallelogram ABCD, find x.
a. 4 c. 16
b. 10.25 d. 21.5
____ 16. Which of the following is a property of a parallelogram?
a. The diagonals are congruent. c. The diagonals are perpendicular.
b. The diagonals bisect the angles. d. The diagonals bisect each other.
____ 17. Find x and y so that ABCD will be a parallelogram.
a. x = 6, y = 42 c. x = 20, y = 42
b. x = 6, y = 22 d. x = 20, y = 22
____ 18. Find x so that this quadrilateral is a parallelogram.
a. 44 c. 90
b. 46 d. 134
Name: ________________________ ID: A
4
____ 19. Parallelogram ABCD has vertices A(0, 0), B(2, 4), and C(10, 4). Find the possible coordinates of D.
a. (8, 0) c. (0, 4)
b. (10, 0) d. (10, 8)
____ 20. Which of the following is a property of all rectangles?
a. four congruent sides c. diagonals are perpendicular
b. diagonals bisect the angles d. four right angles
____ 21. ABCD is a rectangle with diagonals AC and BD. If AC = 2x + 10 and BD = 56, find x.
a. 23 c. 78
b. 33 d. 122
____ 22. ABCD is a rectangle with B(−5, 0), C(7, 0) and D(7, 3). Find the coordinates of A.
a. (−5, 7) c. (−5, 3)
b. (3, 5) d. (7, −3)
____ 23. For rhombus ABCD, find m∠1.
a. 45 c. 90
b. 60 d. 120
____ 24. Find m∠PRS in square PQRS.
a. 30 c. 60
b. 45 d. 90
____ 25. Choose a pair of base angles of trapezoid ABCD.
a. ∠A, ∠C c. ∠A, ∠D
b. ∠B, ∠D d. ∠D, ∠C
____ 26. In trapezoid DEFG, find m∠D.
a. 44 c. 108
b. 72 d. 136
Name: ________________________ ID: A
5
____ 27. The hood of Olivia’s car is the shape of a trapezoid. The base bordering the windshield measures 30 inches
and the base at the front of the car measures 24 inches. What is the width of the median of the hood?
a. 25 in. c. 28 in.
b. 27 in. d. 29 in.
____ 28. The length of one base of a trapezoid is 44, the median is 36, and the other base is 2x + 10. Find x.
a. 9 c. 21
b. 17 d. 40
____ 29. Given trapezoid ABCD with median EF, which of the following is true?
a. EF =1
2AD c. AB = EF
b. AE = FD d. EF =BC + AD
2
____ 30. ABCD is a rectangle with A(0, 0), B(b, 0), and D(0, a). Find the coordinates of C.
a. C(a, b) c. C(2b, a)
b. C(b, a) d. C(a + b, a)
____ 31. To prove that the diagonals of a square bisect each other, you would position and label a square in the
coordinate plane and then find which of the following?
a. measures of the angles c. lengths of the diagonals
b. midpoints of the diagonals d. slopes of the diagonals
____ 32. Find the sum of the measures of the interior angles of a convex 45-gon.
a. 8100 c. 360
b. 7740 d. 172
____ 33. Find x.
a. 30 c. 102
b. 66 d. 138
____ 34. Find the sum of the measures of the exterior angles of a convex 39-gon.
a. 39 c. 180
b. 90 d. 360
____ 35. Which of the following is a property of a parallelogram?
a. Each pair of opposite sides is congruent.
b. Only one pair of opposite angles is congruent.
c. Each pair of opposite angles is supplementary.
d. There are four right angles.
Name: ________________________ ID: A
6
____ 36. For parallelogram ABCD, find m∠1.
a. 60 c. 36
b. 54 d. 18
____ 37. ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find x.
a. 5 c. 27
b. 17 d. 47
____ 38. Find x and y so that this quadrilateral is a parallelogram.
a. x = 13, y = 24 c. x = 7, y = 24
b. x = 13, y = 6 d. x = 7, y = 6
____ 39. Find x so that this quadrilateral is a parallelogram.
a. 12 c. 36
b. 24 d. 132
____ 40. Parallelogram ABCD has vertices A(8, 2), B(6, −4), and C(−5, −4). Find the coordinates of D.
a. D(−5, 2) c. D(−2, 2)
b. D(−3, 2) d. D(−4, 8)
____ 41. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find x.
a. 5 c. 11
b. 6 d. 26
____ 42. Which of the following is true for all rectangles?
a. The diagonals are perpendicular. c. The consecutive sides are congruent.
b. The diagonals bisect the angles. d. The consecutive sides are perpendicular.
____ 43. ABCD is a rectangle with B(−4, 6), C(−4, 2), and D(10, 2). Find the coordinates of A.
a. A(6, 4) c. A(2, 6)
b. A(10, 4) d. A(10, 6)
Name: ________________________ ID: A
7
____ 44. For rhombus GHJK, find m∠1.
a. 22 c. 68
b. 44 d. 90
____ 45. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x − 10, find AC.
a. 11 c. 56
b. 28 d. 90
____ 46. ABCD is an isosceles trapezoid with A(10, −1), B(8, 3), and C(−1, 3). Find the coordinates of D.
a. (−3, −1) c. (−1, 8)
b. (−10, −11) d. (−3, 3)
____ 47. For isosceles trapezoid MNOP, find m∠MNP.
a. 44 c. 80
b. 64 d. 116
____ 48. The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length
of the other base.
a. 35 in. c. 17.5 in.
b. 19 in. d. 13 in.
____ 49. Judith built a fence to surround her property. On a coordinate plane, the four corners of the fence are located
at (−16, 1), (−6, 5), (4, 1), and (−6, −3). Which of the following most accurately describes the shape of
Judith’s fence?
a. square c. rhombus
b. rectangle d. trapezoid
____ 50. What type of quadrilateral has vertices at (0, 0), (a, b), (c, b), and (c + a, 0)?
a. parallelogram c. rhombus
b. rectangle d. trapezoid
____ 51. To prove that the diagonals of a rhombus are perpendicular to each other, you would position and label a
rhombus on a coordinate plane and then find which of the following?
a. measures of the angles c. lengths of the diagonals
b. slopes of the diagonals d. midpoints of the diagonals
____ 52. There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples to plums?
a. 3:5 c. 5:3
b. 3:8 d. 8:3
____ 53. The scale drawing of a porch is 8 inches wide by 12 inches long. If the actual porch is 12 feet wide, what is
the length of the porch?
a. 8 ft c. 16 ft
b. 10 ft d. 18 ft
Name: ________________________ ID: A
8
____ 54. Solve 5
6=
4
x.
a. 4.6 c. 5
b. 4.8 d. 7
____ 55. A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample
was representative, find the number of bulbs expected to be defective in a case of 450.
a. 24 c. 36
b. 30 d. 45
____ 56. Find the triangle similar to ABC below
a. c.
b. d.
____ 57. Find x if ABC ~ JKL.
a. 10 c. 25
b. 14 d. 29
____ 58. Quadrilateral ABCD ∼ quadrilateral PQRS. If AB = 10, BC = 6, PS = 12, and QR = 4, find the scale factor of