Name: ________________________ Class: ___________________ Date: __________ ID: R

1

REVIEW: Mid Term Exam 2016-2017____ 1. What other information do you need in order to prove the triangles congruent using the SAS Congruence

Postulate?

A. AB AD C. CBA CDAB. BAC DAC D. AB AD

____ 2. The expressions in the figure below represent the measures of two angles. Find the value of x. f g . The diagram is not to scale.

A. 19 B. 18 C. 20 D. –19____ 3. Line r is parallel to line t. Find m6. The diagram is not to scale.

A. 49 B. 149 C. 131 D. 39

Name: ________________________ ID: R

2

____ 4. What is the intersection of plane STXW and plane SVUT?

A. YZ B. TX C. ST D. SV

____ 5. What is the length of BD?

A. 10 B. 11 C. 2 D. 12____ 6. Find the glide reflection image of the black triangle for the composition (Rx 1 T 0,7 ).

A. C.

B. D.

Name: ________________________ ID: R

3

____ 7. What are the names of three planes that contain point A?

A. planes ABDC, ABFE, and ACGEB. planes ABDC, EFGH , and ACGEC. planes CDHG, ABFE, and ACGED. planes ABDC, ABFE, and CDHG

____ 8. Name an angle vertical to DGH.

A. HGI B. HGJ C. HGD D. JGF____ 9. What is the value of x?

A. 78° B. 73° C. 146° D. 156°

Name: ________________________ ID: R

4

In the diagram, figure RQTS is the image of figure DEFC after a rigid motion.

____ 10. Name the image of F.A. Q B. R C. T D. S

____ 11. Name the image of EF .A. ST B. RS C. QR D. TQ

____ 12. What are the names of four coplanar points?

A. Points P, M , N , and C are coplanar.B. Points P, M , D, and C are coplanar.C. Points F, D, P, and N are coplanar.D. Points P, M , F, and C are coplanar.

Name: ________________________ ID: R

5

____ 13. What are the names of three collinear points?

A. Points X , U , and Y are collinear. C. Points Z, U , and Y are collinear.B. Points V , U , and T are collinear. D. Points Z, U , and T are collinear.

____ 14. Identify the hypothesis and conclusion of this conditional statement:If today is Wednesday, then tomorrow is Thursday.A. Hypothesis: Tomorrow is Thursday.

Conclusion: Today is Wednesday.B. Hypothesis: Today is Wednesday.

Conclusion: Tomorrow is not Thursday.C. Hypothesis: Tomorrow is not Thursday.

Conclusion: Today is Wednesday.D. Hypothesis: Today is Wednesday.

Conclusion: Tomorrow is Thursday.____ 15. Find the values of x and y.

A. x 90, y 41 C. x 41, y 49B. x 90, y 49 D. x 49, y 41

____ 16. Write an equation in point-slope form of the line through point J(4, 1) with slope –5.A. y 1 5 x 4 C. y 1 5 x 4 B. y 1 5 x 4 D. y 1 5 x 4

Name: ________________________ ID: R

6

____ 17. What conjecture can you make about the twentieth term in the pattern A, B, A, C, A, B, A, C?A. The twentieth term is A. C. The twentieth term is B.B. The twentieth term is C. D. There is not enough information.

____ 18. When a conditional and its converse are true, you can combine them as a true ____.A. hypothesis C. counterexampleB. unconditional D. biconditional

____ 19. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent?

A. either SAS or AAS C. AAS onlyB. SAS only D. neitherThe hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles.

____ 20. What is r (240,O)(G)?A. I B. P C. O D. K

Name: ________________________ ID: R

7

____ 21. Find the value of x. The diagram is not to scale.

A. 44 B. 78 C. 136 D. 148____ 22. Write an equation in slope-intercept form of the line through point P(7, –2) with slope –3.

A. y + 7 = –3(x – 2) C. y = –3x + 19B. y = –3x – 2 D. y + 2 = –3(x – 7)

____ 23. What is the relationship between 2 and 7?

A. same-side interior angles C. alternate interior anglesB. alternate exterior angles D. corresponding angles

Name: ________________________ ID: R

8

____ 24. Which graph shows T 3,3 ( ABC) ?

A. C.

B. D.

Name: ________________________ ID: R

9

____ 25. If Z is the midpoint of RT , what are x, RZ, and RT?

A. x = 5, RZ = 3, and RT = 6 C. x = 9, RZ = 9, and RT = 18B. x = 7, RZ = 9, and RT = 18 D. x = 7, RZ = 18, and RT = 9

____ 26. If EF 9 and EG 28, find the value of FG. The drawing is not to scale.

A. 18 C. 21B. 9 D. 19

____ 27. What is the graph of y = 12x + 1?

A. C.

B. D.

Name: ________________________ ID: R

10

____ 28. Name the theorem or postulate that lets you immediately conclude ABD CBD.

A. SAS B. ASA C. AAS D. none of these____ 29. Which two lines are parallel?

I. 3y 2x 3II. 3y 1 2xIII. 4y 3x 1

A. I and III C. II and IIIB. I and II D. No two of the lines are parallel.

____ 30. If mEOF 40 and mFOG 27, then what is the measure of EOG? The diagram is not to scale.

A. 80 B. 67 C. 54 D. 13____ 31. What is the name of the ray that is opposite OP ?

A. MP B. OM C. OP D. NP

Name: ________________________ ID: R

11

____ 32. Which lines are parallel if m2 m8? Justify your answer.

A. r s, by the Converse of the Same-Side Interior Angles PostulateB. l m, by the Converse of the Alternate Interior Angles TheoremC. l m, by the Converse of the Same-Side Interior Angles PostulateD. r s, by the Converse of the Alternate Interior Angles Theorem

____ 33. What are the measures of EBF and DBH ? Classify each angle as acute, right, obtuse, or straight.

A. mEBF 10; EBF is obtuse.mDBH 128; DBH is acute.

B. mEBF 20; EBF is acute.mDBH 128; DBH is obtuse.

C. mEBF 10; EBF is acute.mDBH 128; DBH is obtuse.

D. mEBF 10; EBF is acute.mDBH 118; DBH is obtuse.

____ 34. What is a counterexample for the conjecture?Conjecture: The product of two positive numbers is greater than the sum of the two numbers.A. There is no counterexample. The conjecture is true.B. 2 and 2C. 3 and 5D. A counterexample exists, but it is not shown above.

Name: ________________________ ID: R

12

____ 35. What is a counterexample for the conjecture?Conjecture: Any number that is divisible by 6 is also divisible by 12.A. 48 B. 36 C. 30 D. 60Use the diagram to find the following.

____ 36. What are three pairs of corresponding angles?A. angles 2 & 4, 3 & 5, and 1 & 8 C. angles 1 & 2, 5 & 6, and 4 & 7B. angles 4 & 7, 5 & 6, and 1 & 2 D. angles 3 & 5, 1 & 7, and 8 & 6

____ 37. Identify a pair of alternate exterior angles.A. 1 and5 C. 2 and5B. 8 and4 D. 1 and8

____ 38. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

A. Yes; ACB ACD.B. Yes; ABC ACD.C. Yes; CAB DAC .D. No, the triangles cannot be proven congruent.

Name: ________________________ ID: R

13

____ 39. What four segments are parallel to plane MRQL?A. segments JK, KL, JM, and ML C. segments NP, KP, PQ, and JNB. segments JK, JN, NP, and KP D. segments JM, KL, NR, and PQ

____ 40. What four segments are perpendicular to plane KLMJ?A. segments MR, LQ, NR and PQ C. segments MR, LQ, KP, and JNB. segments NP, RQ, KP, and JN D. segments PQ, QR, NR, and NP

____ 41. Judging by appearance, name an acute angle, an obtuse angle, and a right angle.

A. D, E, C C. A, B, EB. C, D, B D. A, C, E

____ 42. A triangular playground has angles with measures in the ratio 5 : 4 : 6. What is the measure of the smallest angle?A. 58 B. 48 C. 10 D. 38

Name: ________________________ ID: R

14

____ 43. Justify the last two steps of the proof.Given: MN PO and MO PNProve: MNO PON

Proof:1. MN PO 1. Given2. MO PN 2. Given3. NO ON 3. ?4. MNO PON 4. ?A. Symmetric Property of ; SSS C. Reflexive Property of ; SASB. Symmetric Property of ; SAS D. Reflexive Property of ; SSS

____ 44. What are the names of the segments in the figure?

A. The three segments are AB, BC , and BA.B. The two segments are AB and BC .C. The three segments are AB, BC , and AC.D. The three segments are AB, CA, and AC .

Name: ________________________ ID: R

15

____ 45. Which graph shows a triangle and its reflection image over the x-axis?A. C.

B. D.

____ 46. Use the Law of Syllogism to draw a conclusion from the two given statements.If you exercise regularly, then you have a healthy body.If you have a healthy body, then you have more energy.A. If you do not have more energy, then you do not exercise regularly.B. You have more energy.C. You have a healthy body.D. If you exercise regularly, then you have more energy.

Name: ________________________ ID: R

16

____ 47. Name the line and plane shown in the diagram.

A. MN and plane M NP C. NM and plane POB. line M and plane M NP D. MN and plane PM

____ 48. Find the value of k. The diagram is not to scale.

A. 43 B. 101 C. 108 D. 79____ 49. Name the angle included by the sides NM and MP.

A. M B. P C. N D. none of these

Name: ________________________ ID: R

17

____ 50. Which pair of triangles is congruent by ASA?A. C.

B. D.

____ 51. The vertices of a triangle are P(7, 5), Q(5, 8), and R(–8, –7). Name the vertices of R y 0( PQR).A. P (7, 5), Q (5, 8), R(8, 7) C. P (7, 5), Q (5, 8), R(8, 7)B. P (7, 5), Q(5, 8), R(8, 7) D. P (7, 5), Q (5, 8), R(8, 7)

____ 52. Describe in words the translation of X represented by the translation rule T 1,7 (X).A. 1 units to the left and 7 units downB. 1 units to the right and 7 units upC. 7 units to the left and 1 units upD. 1 units to the right and 7 units down

____ 53. Which triangles are congruent by ASA?

A. ABC andTUV C. VTU andHGFB. VTU andABC D. none

Name: ________________________ ID: R

18

____ 54. Name the ray in the figure.

A. MN B. NM C. MN D. NM

____ 55. If MNO PQR, which of the following can you NOT conclude as being true?A. M P B. MN PR C. NO QR D. N Q

____ 56. Find the value of x. l m. The diagram is not to scale.

A. 162 B. 54 C. 126 D. 18____ 57. Find mG. p r. The diagram is not to scale.

A. 104 B. 140 C. 40 D. 116____ 58. Which statement provides a counterexample to the following faulty definition?

A square is a figure with four congruent sides.A. Some triangles have all sides congruent.B. A square has four congruent angles.C. A six-sided figure can have four sides congruent.D. A rectangle has four sides.

Name: ________________________ ID: R

19

____ 59. Supply the missing reasons to complete the proof.Given: R U and RT UTProve: ST VT

Statement Reasons1. R U andRT UT

1. Given

2. STR VTU 2. Vertical angles are congruent.3. STR VTU 3. ?4. ST VT 4. ?

A. AAS; Corresp. parts of are . C. SAS; Corresp. parts of are .B. ASA; Corresp. parts of are . D. ASA; Substitution

____ 60. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.Statement 1: If x = 3, then 9x – 10 = 17.Statement 2: x = 3A. x = 3 C. 9x – 10 = 17B. If 9x – 10 = 17, then x = 3. D. not possible

____ 61. If EF 4x 15, FG 3x 7, and EG 27, find the values of x, EF, and FG. The drawing is not to scale.

A. x = 7, EF = 43, FG = 28 C. x = 8, EF = 17, FG = 17B. x = 8, EF = 13, FG = 14 D. x = 7, EF = 13, FG = 14

____ 62. Are points C, G, and H collinear or noncollinear?

A. noncollinear B. collinear C. impossible to tell

Name: ________________________ ID: R

20

____ 63. Name the plane represented by the front of the box.

A. CAB B. GBF C. BJC D. DBF____ 64. Name the intersection of plane ACG and plane BCG.

A. AC C. CG

B. BG D. The planes need not intersect.____ 65. What plane contains points C, D, and G?

A. The plane on the bottom of the figure.B. The plane on the top of the figure.C. The plane on the front of the figure.D. The plane that passes at a slant through the figure.

____ 66. If EF 4x 15, FG 39, and EG 110, find the value of x. The drawing is not to scale.

A. x 56 C. x 14B. x 16 D. x 2

____ 67. If EG 25, and point F is 2/5 of the way between E and G, find the value FG. The drawing is not to scale.

A. 12.5 C. 15B. 10 D. 20

____ 68. Which point is the midpoint of AE?

A. D B. B C. not B, C, or D D. C

Name: ________________________ ID: R

21

____ 69. If T is the midpoint of SU , what are ST, TU, and SU?

A. ST = 7, TU = 63, and SU = 126 C. ST = 18, TU = 18, and SU = 36B. ST = 80, TU = 80, and SU = 160 D. ST = 63, TU = 63, and SU = 126

____ 70. Complete the statement.

GDF ? A. DGF C. EDF B. DEF D. DFE

____ 71. If mAOC 85, mBOC 2x 10, and mAOB 4x 15, find the degree measure of BOC andAOB. The diagram is not to scale.

A. mBOC 30; mAOB 55 C. mBOC 45; mAOB 40B. mBOC 40; mAOB 45 D. mBOC 55; mAOB 30

Name: ________________________ ID: R

22

____ 72. Name an angle supplementary to COD.

A. BOD B. COA C. AOE D. COB____ 73. Name an angle adjacent to DGE.

A. FGI B. EGH C. HGJ D. JGI____ 74. Supplementary angles are two angles whose measures have a sum of ____.

Complementary angles are two angles whose measures have a sum of ____.A. 90; 180 B. 90; 45 C. 180; 360 D. 180; 90

Name: ________________________ ID: R

23

____ 75. In the figure shown, mAED 121. Which of the following statements is false?

Not drawn to scaleA. mAEB 59B. BEC and AED are vertical angles.C. AEB and BEC are vertical angles.D. mBEC 121

____ 76. Find the circumference of the circle to the nearest tenth. Use 3.14 for .

A. 78.5 m B. 314 m C. 1962.5 m D. 157 m____ 77. Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam

the garden with greatest area? The diagrams are not to scale.A. C.

B. D.

Name: ________________________ ID: R

24

____ 78. Based on the pattern, what are the next two terms of the sequence?9, 15, 21, 27, . . .A. 33, 972 B. 39, 45 C. 162, 972 D. 33, 39

____ 79. What conjecture can you make about the sum of the first 40 positive even numbers?2 = 2 = 1 22 + 4 = 6 = 2 32 + 4 + 6 = 12 = 3 42 + 4 + 6 + 8 = 20 = 4 52 + 4 + 6 + 8 + 10 = 30 = 5 6A. The sum is 39 40. C. The sum is 40 41.B. The sum is 41 42. D. The sum is 40 40.

____ 80. Alfred is practicing typing. The first time he tested himself, he could type 45 words per minute. After practicing for a week, he could type 48 words per minute. After two weeks he could type 51 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice.A. 61 words per minute C. 54 words per minuteB. 57 words per minute D. 51 words per minute

____ 81. What is the conclusion of the following conditional?A number is divisible by 2 if the number is even.A. The sum of the digits of the number is divisible by 2.B. If a number is even, then the number is divisible by 2.C. The number is even.D. The number is divisible by 2.

____ 82. Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ , and the part following then is the ____.A. conditional; conclusion; hypothesis C. conditional; hypothesis; conclusionB. hypothesis; conclusion; conditional D. hypothesis; conditional; conclusion

____ 83. Write this statement as a conditional in if-then form:All triangles have three sides.A. If a triangle has three sides, then all triangles have three sides.B. If a figure has three sides, then it is not a triangle.C. If a figure is a triangle, then all triangles have three sides.D. If a figure is a triangle, then it has three sides.

____ 84. What is the converse of the following conditional?If a point is in the fourth quadrant, then its coordinates are negative.A. If a point is in the fourth quadrant, then its coordinates are negative.B. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.C. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.D. If the coordinates of a point are negative, then the point is in the fourth quadrant.

Name: ________________________ ID: R

25

____ 85. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.If an angle is a right angle, its measure is 90.If an angle measure is 90, the angle is a right angle.A. One statement is false. If an angle measure is 90, the angle may be a vertical angle.B. One statement is false. If an angle is a right angle, its measure may be 180.C. Both statements are true. An angle is a right angle if (and only if) its measure is 90.D. Both statements are true. The measure of angle is 90 if (and only if) it is not a right

angle.____ 86. Which angles are corresponding angles?

A. 7 and3 C. 3 and11B. 8 and3 D. none of theseThis diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.

____ 87. How are 8 and 4 related?A. alternate interior angles C. same-side interior anglesB. corresponding angles D. none of these

____ 88. If 8 measures 127, what is the sum of the measures of 1 and 4?A. 254 B. 307 C. 127 D. 106

Name: ________________________ ID: R

26

____ 89. Find mP. The diagram is not to scale.

A. 106 B. 74 C. 64 D. 84____ 90. Which lines are parallel if m1 m2 180? Justify your answer.

A. j k , by the Converse of the Same-Side Interior Angles PostulateB. j k , by the Converse of the Alternate Interior Angles TheoremC. g h , by the Converse of the Alternate Interior Angles TheoremD. g h , by the Converse of the Same-Side Interior Angles Postulate

____ 91. Find the value of x for which p is parallel to q, if m1 (9x) and m3 117.The diagram is not to scale.

A. 108 B. 13 C. 117 D. 126____ 92. Find the value of x for which l is parallel to m. The diagram is not to scale.

A. 100 B. 80 C. 123 D. 41

Name: ________________________ ID: R

27

____ 93. Find the value of x. The diagram is not to scale.Given: SRT STR, mSRT 28, mSTU 2x

A. 28 B. 30 C. 14 D. 76____ 94. Find the value of x. The diagram is not to scale.

A. 33 B. 70 C. 23 D. 13____ 95. If BCDE is congruent to OPQR, then DE is congruent to ? .

A. PQ B. OR C. OP D. QR____ 96. Given QRS TUV, QS 3v 2, and TV 7v 6, find the length of QS and TV.

A. 2 B. 9 C. 8 D. 20____ 97. Given ABC PQR, mB 3v 4, and mQ 8v 6, find mB and mQ.

A. 22 B. 11 C. 10 D. 25

Name: ________________________ ID: R

28

____ 98. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale.

A. 4 B. 5 C. 3 D. 38

Name: ________________________ ID: R

29

____ 99. Which graph shows T 4,2 ( ABC)?

A. C.

B. D.

Name: ________________________ ID: R

30

Use the diagram.

____ 100. Find the image of C under the translation described by the translation rule T 4,5 (C).A. B B. E C. A D. D

____ 101. Use a translation rule to describe the translation of X that is 5 units to the left and 7 units up.A. T 5,7 (X) C. T 5,7 (X)B. T 5,7 (X) D. T 5,7 (X)

____ 102. Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1. Write a rule to describe the translation needed to put her in the proper seat.A. T<-8,2>(Jessica) C. T<-8,-2>(Jessica)B. T<8,2>(Jessica) D. T<8,-2>(Jessica)

____ 103. What is a rule that describes the translation ABCD ABC D ?

A. T 3,2 (ABCD) C. T 2,3 (ABCD)B. T 3,2 (ABCD) D. T 3,2 (ABCD)

Name: ________________________ ID: R

31

____ 104. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of Rx 0 ( PQR).A. P (2, 4), Q (2, 5), R(1, 8) C. P (2, 4), Q (2, 5), R(1, 8)B. P (2,4), Q (2,5), R(1,8) D. P (2, 4), Q(2, 5), R(1, 8)

105. Draw Rx-axis (ABC).

106. Graph points A(1, 5), B(5, 2), and C(1, 2). Graph R y 0( ABC).

Name: ________________________ ID: R

32

107. J is the midpoint of both KC and LB. How can you use the properties of rotations to show that KL and CB are equal lengths?