Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12)

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1 Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Use the figure at the right for # What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane BAC 2. Which segment is on line n? A. AD B. BC C. AD D. BE 3. Which is the name of a ray with endpoint A? A. DA B. BC C. CA D. AB 4. Name the intersection of plane P and line m? A. line n B. point A C. AC D. AE 5. What is the measure of RT? A. 5 B. 16 C. 26 D. 40 Use the figure at the right for # Which term describes PMQ? A. obtuse B. straight C. right D. acute 7. What is m PMN? A. 22 B. 90 C. 68 D. 112

2 8. AB bisects CAD. Find x. A. 2 B. 6 C. 4 D X is the midpoint of WY. Find WX. A. 1 B. 6 C. 4 D Two angles are supplementary. If m 1 = 67, what is m 2? 11. Find the measure of the complement of T, where m T = Reflect the figure with the given vertices across x-axis. A(-4, 1), B (2, 4), C (3, -2) A B C

3 13. Translate the figure with the given vertices along the vector <2, 3>. A (-2, 1), B (4, 3), C (2, -2) A B C 14. Rotate the figure with the given vertices about the origin with a counterclockwise 90 angle of rotation. A (2, 3), B (-2, 1), C (1, -1) A B C 15. Does the figure have line symmetry? If yes, draw all lines. Does the figure have rotational symmetry? If yes, give the angle of rotation and order of symmetry. Angle Order

4 16. Given GH with endpoints G (-11, 4) and H (-1, -9), what are the coordinates of the midpoint of GH? A. (-12, -5) B. (-6, -2.5) C. (-10, 13) D. (-5, 6.5) 17. M is the midpoint of RS. R has coordinates (-12, 4) and M has coordinates (1, -2). What are the coordinates of S? A. (-5.5, -1) B. (-11, 2) C. (13, 6) D. (14, -8) 18. What is the distance from M (-1, 6) to N (11, 1)? A. 12 units B. 149 units C. 13 units D. 169 units 19. What is the distance from V to W? A. 17 cm B. 23 cm C. 120 cm D. 289 cm 20. What transformation is shown? A. rotation B. reflection C. translation D. image 21. Given a point in the coordinate plane, the rule (x, y) (x + 2, y - 3) translates the point in which direction? A. 2 units to the left and 3 units up B. 3 units to the left and 2 units down C. 3 units right and 2 units up D. 2 units to the right and 3 units down 22. Which is the biconditional statement of the conditional statement If x 3 = -1, then x = -1? A. If x = -1, then x 3 = -1 B. x 3 = -1 if x = -1 C. x 3 = -1 if and only if x = -1 D. x = -1 x 3 = -1

5 23. For which statement is the converse false? A. If Mary can swim, then she can swim the crawl. B. If it is raining outside, then the temperature is above freezing. C. If Greg has two children, then he has one son and one daughter. D. If Caroline can stand up, then she can walk. 24. Which is a counterexample of the statement? If an animal has wings, then it can fly. A. penguin B. robin C. duck D. rabbit 25. Write a conditional statement of the biconditional statement An angle is an acute angle if and only if the angle s measure is less than Fill in the reasons. 5 = 2 ½x Given 2 ½x = 5 2(2- ½x) = 10 4 x = 10 -x = 6 x = Given: BD bisects ABC Prove: BG bisects FBH Statements Reasons 1. BD bis. ABC m 1 = m m 1 = m m 4 = m m 2 = m m 4 = m BG bisects FBH 7.

6 Use the figure at the right for # Classify EH and DH A. skew B. parallel C. perpendicular D. none of these 29. How many segments are skew to AE? A. 1 B. 2 C. 3 D. 4 Use the figure at the right for # Which are alternate interior angles? A. 1 & 3 B. 1 & 8 C. 3 & 6 D. 6 & Which statement is true? A. 1 and 2 are alternate interior angles. B. 1 and 3 are corresponding angles. C. 3 and 6 are alternate exterior angles. D. 3 and 7 are same-side interior angles. 32. Which correctly completes the sentence? If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are. A. supplementary B. complementary C. corresponding D. congruent 33. What type of angle is 1? A. acute B. right C. obtuse D. straight 34. Given RS QP, what is the value of x? A. 6 B. 9 C. 72 D. 108

7 Use the figure at the right for # Which information proves that r s? A. 1 3 B. 4 5 C. 4 6 D If m 3 = (4x + 20) and m 5 = (6x + 10), what value of x proves that r s? A. 5 B. 15 C. 40 D If a transversal is perpendicular to one of two parallel lines, how many different angle measures are formed? A. 1 B. 3 C. 4 D Which is a possible value of x? A. -2 B. 1 C. 3 D Which describes the slope of a horizontal line? A. positive B. negative C. zero D. undefined 40. What is the slope of a line through (-1, 4) and (5, 2)? A. -3 B. ½ C D Given A (1, 5), B (-2, -1), C (1, 1) and D (3, 5), what type of lines are AB and CD? A. parallel B. perpendicular C. horizontal D. vertical 42. Which is the equation of the line through (1, 11) and (-2, 2)? A. y = 3x - 8 B. y = 3 1 x + 8 C. 3x + y = 8 D. -3x + y = 8

8 43. Classify the triangle. A. isosceles acute B. isosceles obtuse C. scalene acute D. scalene obtuse 44. What is m KLM? A. 3 B. 22 C. 42 D What is the m U? A. 5 B. 15 C. 40 D Two congruent triangles have the following corresponding parts: RS UV, RT UW, and R U. Which is NOT necessarily a correct congruence statement? A. RST UVW B. STR VWU C. TRS VWU D. TRS WUV 47. KLM RST, m L = (3x + 15) and m S = (6x + 3). What is the value of x? A. 2 B. 4 C. 6 D. 27 Use the figure at the right for # If AD = 5y + 7 and BC = 7y - 3, what must the value of y be to prove AED CEB by the SSS postulate? A. 2 B. 5 C. 17 D What postulate or theorem justifies the congruence statement ABE CDE? A. SSS B. ASA C. SAS D. AAS

9 50. What method proves the triangles are congruent? A. SSS B. SAS C. HL D. AAS 51. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. A. ABC DEC; SAS B. ABC DEC; AAS C. BAC CED; AAS D. BAC CED; SSS 52. Find CA. 53. Find a, b, and c. 54. What is the value of x? A. 12 B C. 18 D. 60

10 Use the partially completed proof for #55-57 Given: l m, 1 3 Prove: r p Statements 1. l m 1. Given Reasons Corresponding angles postulate r p Which reason belongs in step 3? A. transitive property of congruence B. given C. corresponding angle postulate D. converse of alternate exterior angle theorem 56. Which reason belongs in step 4? A. transitive property of congruence B. given C. corresponding angle postulate D. converse of alternate exterior angle theorem 57. Which reason belongs in step 5? A. transitive property of congruence B. given C. corresponding angle postulate D. converse of alternate exterior angle theorem 58. Find x

11 59. Find m A. 60. Find x. 61. The ratio of the side lengths of a triangle is 3 : 4 : 5. What could NOT be the side lengths of the triangle? A. 1.5 in., 2 in., 2.5 in. B. 4.5 in., 6 in., 7.5 in. C. 7.5 in., 10.5 in., 12.5 in. D in., 11 in., in. x 3 2x What is the value of x? 12 8 A. 81 B. 9 C. 4.5 D. Not here 63. If 21x = 63y, what is the ratio of x to y expressed in simplest form? A. B. C. D The ratio of a dog park s length to its width is 11 : 9. If the width of the field is 180 yards, what is the length of the field? If necessary, round to the nearest whole number. A. 147 feet B. 220 feet C feet D. not here 65. Which similarity statement is true for rectangles JKLM and PQRS given that JK = 6, JM = 5, QR = 15, and PQ = 12.5? A. rectangle JKLM ~ rectangle PQRS B. rectangle JKLM ~ rectangle QRSP C. rectangle JKLM ~ rectangle RQPS D. rectangle JKLM ~ rectangle SRQP 66. JKL ~ MNO. The similarity ratio of JKL to MNO is 5 : 2. What is the length of MN? A. 6 B C. 14 D. 37.5

12 67. Which similarity postulate or theorem lets you conclude that ABC ~ CDE? A. AA B. SAS C. SSS D. Triangles are not similar 68. What is ST? A B. 20 C D What information guarantees that XY AC? A. XB = 20, BY = 25 B. XB = 24, BY = 30 C. XB = 25, BY = 20 D. XB = 32, BY = In JKL, the bisector of J divides KL into XK with length (y + 3) and XL with length (2y). If JK = 12 and JL = 16, which could be the length of XK? A. 6 B. 9 C. 12 D A student who is 60 inches tall measured shadows to find the height of a tree. The student s shadow was 24 inches long and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches? x 60 x A. B. C. D. 156 x 13 x A blueprint uses a scale of 1.5 in. : 24 ft. If the actual room has a width of 12 yards and a length of 17 yards, how long is the room in blueprint? A in B in C in D in

13 73. Verify PQR and PRS are similar. 74. Verify JKL and JMN are similar. 75. Find EF to the nearest tenth. 76. Find x.

14 77. Which is NOT a correct classification for the triangle? A. acute B. isosceles C. equiangular D. scalene 78. What is the length of side BC? A. 8 B. 6 C. 10 D Given the perimeter of ABC = 12 feet, find perimeter of XYZ. 80. Given the area of ABC = 6 feet 2, find the area of XYZ.

15 Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Vocabulary - Matching Match each vocabulary term with its definition. A. ray B. coplanar C. segment bisector D. complementary angles E. biconditional F. congruent angles G. acute angle H. postulate I. obtuse angle J. supplementary angles K. linear pair L. parallel lines M. perpendicular lines N. skew lines O. theorem P. equilateral triangle Q. slope R. isosceles triangle S. equiangular triangle T. scale factor U. CPCTC V. similar polygons W. reflexive prop. X. transitive prop. Y. proportion 1. points that lie in the same plane 2. a statement that is accepted without proof, an axiom 3. a part of a line that starts at an endpoint and extends forever in one direction 4. a segment, ray, or line which divides a segment into two congruent parts 5. angles that have the same measure 6. an angle that measures greater than 0 and less than an angle that measures greater than 90 and less than two angles whose measures have a sum of a pair of adjacent angles whose noncommon sides are opposite rays which form a line 10. a statement that can be written in the form p if and only if q 11. two angles whose measures have a sum of lines that do not intersect and are not in the same plane 13. lines in the same plane that do not intersect 14. lines that intersect at 90 angles 15. a statement that has been proven 16. the measure of the steepness of a line 17. a triangle with three congruent sides 18. a triangle with at least two congruent sides 19. a triangle with three congruent angles 20. the ratio of two corresponding linear measurements in a pair of similar figures 21. an equation that states two ratios are equal 22. two polygons whose corresponding angles are congruent and whose corresponding sides are proportional 23. AB = AB and m 1 = m if a = b and b = c, then a = c 25. an abbreviation for corresponding parts of congruent triangles are congruent that is used as a reason in proof after two triangles are proven congruent

16 Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Extended Response 1. Neatly draw and label plane XYZ. Then draw MN intersecting the plane at point P. 2. Neatly draw and label plane XYZ. Then draw intersecting lines n and m contained in the plane. 3. Given the conditional, write the converse and biconditional statement. Determine the truth value of each. The measure of a straight angle is equal to 180. Truth value: Converse: Truth value: Biconditional: Truth value:

17 4. Why are the triangles similar? Find PV. 5. Complete the proof. Given : Prove: M is the midpoint of PQ and QR PS RS Statements Reasons