# Honors Geometry Mid-Term Exam Review

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1 Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The diagram is not to scale. 5. DF bisects EDG. Find FG. The diagram is not to scale. a. straight b. equilateral c. isosceles d. scalene 2. Find the perimeter of the rectangle. The drawing is not to scale. a. 158 feet b. 79 feet c. 107 feet d. 130 feet 3. Supplementary angles are two angles whose measures have sum. Complementary angles are two angles whose measures have sum. a. 90; 180 b. 180; 90 c. 90; 45 d. 180; Find the values of a and b.the diagram is not to scale. a. 23 b. 22 c. 44 d The complement of an angle is 59. What is the measure of the angle? a. 41 b. 131 c. 31 d Which statement is an example of the Subtraction Property of Equality? a. If c = d then c+ e= d+ e b. c = d c. If c = d then c e= d e d. If c = d then c e= d e. 8. Find the distance between points P(7, 1) and Q(4, 6) to the nearest tenth. a. 34 b. 8 c. 5.8 d. 13 a. a = 126, b = 54 b. a = 126, b = 50 c. a = 130, b = 54 d. a = 130, b = 50 1

2 9. List the sides in order from shortest to longest. The diagram is not to scale. 12. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38 and the two congruent sides each measure 21 units? a. JK, LJ, LK b. JK, LK, LJ c. LK, JK, LJ d. LK, LJ, JK 10. Find the value of x. a. 71 b. 152 c. 142 d Complete the statement. If a transversal intersects two parallel lines, then. a. same-side interior angles are complementary b. alternate interior angles are congruent c. corresponding angles are supplementary d. none of these 14. Find the values of x and y. a. 5 b. 7 c. 9 d LMNO is a parallelogram. If NM = x + 9 and OL = 2x + 6 find the value of x and then find NM and OL. a. x = 90, y = 56 b. x= 90, y= 34 c. x = 34, y = 56 d. x= 56, y= 34 a. x = 3, NM = 14, OL = 12 b. x = 5, NM = 12, OL = 14 c. x = 3, NM = 12, OL = 12 d. x = 5, NM = 14, OL = 14 2

3 15. Line r is parallel to line t. Find m 5. The diagram is not to scale. 19. Justify the last two steps of the proof. Given: PQ SR and PR SQ Prove: PQR SRQ a. 146 b. 24 c. 34 d If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. a. x = 19, ST = 75 b. x = 14, ST = 56 c. x = 14, ST = 75 d. x = 19, ST = Write an equation in point-slope form, y y 1 = m(x x 1 ), of the line through points (10, 8) and (9, 2) Use (10, 8) as the point (x 1, y 1 ). a. (y + 8) = 10(x 10) b. (y 8) = 10(x + 10) c. (y + 8) = 10(x 10) d. (y 8) = 10(x + 10) Proof: 1. PQ SR 1. Given 2. PR SQ 2. Given 3. QR RQ 3.? 4. PQR SRQ 4.? a. Reflexive Property of ; SAS b. Symmetric Property of ; SAS c. Symmetric Property of ; SSS d. Reflexive Property of ; SSS 20. Find the value of x. The diagram is not to scale. 18. Find the value of the variable. The diagram is not to scale. a. 61 b. 12 c. 41 d. 22 a. 40 b. 100 c. 68 d. 80 3

4 21. What is the intersection of plane TUYX and plane VUYZ? 25. A triangle has side lengths of 14 cm, 48 cm, and 50 cm. Classify it as acute, obtuse, or right. a. right b. obtuse c. acute 26. Name the smallest angle of ABC. The diagram is not to scale. a. TX b. VZ c. UY d. SW 22. Which three lengths can NOT be the lengths of the sides of a triangle? a. 10 m, 12 m, 10 m b. 16 m, 5 m, 11 m c. 6 m, 10 m, 8 m d. 24 m, 19 m, 15 m 23. Jay, Kay, and Ray found themselves far apart when they stopped for lunch while working in a field. Jay could see Kay, then turn through 66 and see Ray. Kay could see Ray, then turn through 54 and see Jay. Ray could see Jay, then turn through 60 and see Kay. Which two were farthest apart? a. Ray and Jay b. Kay and Ray c. Jay and Kay d. Kay and Ray were the same distance apart as Ray and Jay. 24. The sides of an isosceles triangle have lengths 2x + 2, x + 5. The base has length 2x + 6. What is the length of the base? a. 8 b. 3 c. 12 d. cannot be determined a. Two angles are the same size and smaller than the third. b. B c. A d. C 27. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. a. 13 b. 4 c. 34 d. 17 4

5 Fill in each missing reason. 28. Given: m PQR = x + 7, m SQR = x + 3, and m PQS = 100. Find x. m PQR + m SQR = m PQS x x + 3 = 100 2x + 10 = 100 2x = 90 x = 45 a. b. Substitution Property c. Simplify d. e. Division Property of Equality a. Angle Addition Postulate; Subtraction Property of Equality b. Protractor Postulate; Addition Property of Equality c. Angle Addition Postulate; Addition Property of Equality d. Protractor Postulate; Subtraction Property of Equality 29. Given: 8x 5y= 1; x= 2 Prove: 17 5 = y 8x 5y= 1; x= y= 1 5y= 17 y= 17 5 a. b. c. d. 17 = y e. 5 a. a. Given b. Substitution Property c. Addition Property of Equality d. Division Property of Equality e. Symmetric Property of Equality b. a. Given b. Substitution Property c. Addition Property of Equality d. Addition Property of Equality e. Symmetric Property of Equality c. a. Given b. Substitution Property c. Addition Property of Equality d. Division Property of Equality e. Reflexive Property of Equality d. a. Given b. Symmetric Property of Equality c. Addition Property of Equality d. Division Property of Equality e. Reflexive Property of Equality 5

6 30. If A D and C F, which additional statement does NOT allow you to conclude that ABC DEF? a. BC EF b. AB EF c. B E d. AC DF 31. Given QRS TUV, QS= 5v+ 2, and TV = 7v 8, find the length of QS and TV. a. 28 b. 27 c. 43 d Which three lengths could be the lengths of the sides of a triangle? a. 19 cm, 6 cm, 6 cm b. 13 cm, 9 cm, 22 cm c. 9 cm, 25 cm, 10 cm d. 10 cm, 13 cm, 22 cm 33. DEFG is a rectangle. DF = 3x 5 and EG = x Find the value of x and the length of each diagonal. a. x = 5, DF = 20, EG = 20 b. x = 10, DF = 20, EG = 20 c. x = 10, DF = 25, EG = 28 d. x = 10, DF = 25, EG = In the figure shown, m AED=120. Which of the following statements is false? 35. Noam wants to put a fence around his rectangular garden. His garden measures 31 feet by 36 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose the garden and path? a. 110 ft b. 158 ft c. 79 ft d. 146 ft 36. Find AM in the parallelogram if PN =10 and AO = 6. The diagram is not to scale. a. 12 b. 6 c. 5 d Find the value of x. The diagram is not to scale. Not drawn to scale a. DEC and DEA are vertical angles. b. DEA and AEB are adjacent angles. c. m AEB = 60 d. m BEC = 120 a. x= 22 b. x= 50 c. x= 14 d. none of these 6

7 38. Name the three labeled segments that are parallel to BF. 43. Find the values of the variables in the parallelogram. The diagram is not to scale. a. DH, GH, AE b. CD, AE, DH c. FH, CG, AE, d. CG, AE, DH 39. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. a. x= 39, y= 27, z= 114 b. x= 27, y= 27, z= 153 c. x= 39, y= 27, z= 153 d. x= 27, y= 39, z= Find the values of x and y. a ft b. 65 ft c. 130 ft d ft 40. Find the missing angle measures. The diagram is not to scale. a. x = 120, y = 60 b. x = 60, y = 120 c. x = 30, y = 41 d. x = 41, y = If m EOF = 32 and m FOG = 36, then what is the measure of EOG? The diagram is not to scale. a. x = 115, y = 123 b. x = 66, y = 115 c. x = 66, y = 105 d. x = 105, y = Write an equation for the line perpendicular to y = 2x 13 that contains (1, 10). a. y + 10 = 1 (x 1) b. y + 10 = 2(x 1) c. x = 2(y 1) d. y + 1 = 1 (x 10) The sum of the measures of two exterior angles of a triangle is 277. What is the measure of the third exterior angle? a. 83 b. 73 c. 97 d. 93 a. 4 b. 64 c. 68 d. 72 7

8 46. Find the values of x, y, and z. The diagram is not to scale. 48. If BCDE is congruent to OPQR, then BE is congruent to?. a. OP b. OR c. PQ d. QR 49. Name the theorem or postulate that lets you immediately conclude ABD CBD. a. x = 78, y = 102, z = 62 b. x = 62, y = 102, z = 78 c. x= 78, y= 62, z=102 d. x = 62, y = 78, z = Find the value of x. a. ASA b. AAS c. SAS d. none of these 50. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. a. no; b. yes; c. yes; = 19 2 d. no; = If EF=2x 12, FG= 3x 13, and EG= 25, find the values of x, EF, and FG. The drawing is not to scale. a. 103 b. 19 c. 19 d. 77 a. x = 10, EF = 32, FG = 43 b. x = 1, EF = 10, FG = 10 c. x = 10, EF = 8, FG = 17 d. x = 1, EF = 8, FG = Are U, V, and W collinear? If so, name the line on which they lie. a. No, the three points are not collinear. b. Yes, they lie on the line U X. c. Yes, they lie on the line V X. d. Yes, they lie on the line UW. 8

9 53. Which statement is true? a. All quadrilaterals are squares. b. All quadrilaterals are parallelograms. c. All rectangles are squares. d. All squares are quadrilaterals. 57. Find the values of the variables and the lengths of the sides of this kite. 54. Find the length of AB, given that DB is a median of the triangle and AC = 56. a. x =14, y = 8; 10, 10 b. x = 8, y = 14; 4, 16 c. x =14, y = 8; 4, 16 d. x = 8, y = 14; 10, Classify the polygon by its sides. a. 56 b. 28 c. 112 d. not enough information 55. ABCD is a parallelogram. If m CDA=59, then m DAB=?. The diagram is not to scale. a. octagon b. hexagon c. pentagon d. quadrilateral 59. Find the value of k. The diagram is not to scale. a. 118 b. 121 c. 59 d Name a median for ABC. a. BD b. AD c. CE d. AF a. 21 b. 115 c. 109 d Name the Property of Congruence that justifies the statement: If ST UV, then UV ST. a. Symmetric Property b. Transitive Property c. Reflexive Property d. none of these 9

10 61. What is the name of the segment inside the large triangle? a. perpendicular bisector b. median c. angle bisector d. midsegment 62. Name the Property of Congruence that justifies the statement: If D E and E F, then D F. a. Transitive Property b. Symmetric Property c. Reflexive Property d. none of these 63. Supply the missing reasons to complete the proof. Given: P S and PR SR Prove: QR TR Statement 1. P S and PR SR Reasons 1. Given 2. QRP TRS 2. Vertical angles are congruent. 3. QRP TRS 3.? 4. QR TR 4.? a. ASA; CPCTC b. SAS; CPCTC c. ASA; Substitution d. AAS; CPCTC 64. Write an equation in slope-intercept form of the line through point P( 2, 8) with slope 2. a. y = 2x + 12 b. y 8 = 2(x + 2) c. y = 2x + 8 d. y 2 = 2(x + 8) 10

11 65. Complete the statement. If a transversal intersects two parallel lines, then angles are supplementary. a. same-side interior b. corresponding c. alternate interior d. acute 66. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. b. 67. Find the value of x. The diagram is not to scale. a. 148 b. 73 c. 165 d and 2 are supplementary angles. m 1=x 13, and m 2=x+ 93. Find the measure of each angle. a. 1 = 50, 2 = 130 b. 1 = 50, 2 = 140 c. 1 = 37, 2 = 153 d. 1= 37, 2= Points B, D, and F are midpoints of the sides of ACE. EC = 32 and DF = 25. Find AC. The diagram is not to scale. c. a. 64 b c. 50 d. 32 d. 70. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? a. 18 : 1 b. 1 : 18 c. 9 : 6 d. 6 : Red and grey bricks were used to build a decorative number of red bricks wall. The number of grey bricks was 5 2. There were 175 bricks used in all. How many red bricks were used? a. 25 b. 125 c. 50 d

12 What is the solution of each proportion? a = a. 54 b. 81 c. 9 d. 18 3y 8 12 = y 5 a. 10 b. 7 c d Given the proportion a b = 8, what ratio completes 15 the equivalent proportion a 8 =? a. 15 b b. b 15 c d. a 15 The polygons are similar, but not necessarily drawn to scale. Find the value of x Are the two triangles similar? How do you know? a. x = 8 b. x = 11 2 c. x = 9 d. x = 10 a. yes, by SAS b. yes, by SSS c. yes, by AA d. no 12

13 77. What is the missing reason in the two-column proof? Given: MO bisects PMN and OM bisects PON Prove: PMO MNO Statements Reasons 1. MO bisects PMN 1. Given 2. PMO NMO 2. Definition of angle bisector 3. MO MO 3. Reflexive property 4. OM bisects PON 4. Given 5. POM NOM 5. Definition of angle bisector 6. PMO NMO 6.? a. ASA Postulate b. SSS Postulate c. SAS Postulate d. AAS Theorem 78. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. a. x = 9, y = 18 b. x = 8, y = 9 c. x = 9, y = 8 d. x = 9, y = 33 13

14 79. Supply the reasons missing from the proof shown below. Given: AB AC, BAD CAD Prove: AD bisects BC Statements Reasons 1. AB AC 1. Given 2. BAD CAD 2. Given 3. AD AD 3. Reflexive Property 4. BAD CAD 4.? 5. BD CD 5.? 6. AD bisects BC 6. Def. of segment bisector a. ASA; CPCTC b. SAS; CPCTC c. SSS; Reflexive Property d. SAS; Reflexive Property 14

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