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1 Semester Exam I / Review Integrated Math II 1. Based on the pattern, what are the next two terms of the sequence?,... B. D. 2. 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. 57 words per minute B. 51 words per minute D. 54 words per minute 3. Which choice shows a true conditional, with the hypothesis and conclusion identified correctly? A. Yesterday was Monday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Monday. B. If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is not Thursday. C. Yesterday was Tuesday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday. D. If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday. 4. Draw a Venn diagram to illustrate this conditional: Cars are motor vehicles. A. C. Motor vehicles Cars Cars Motor vehicles

2 B. D. Motor Motor vehicles Cars Cars vehicles 5. Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois. A. Billy Jones lives in Chicago, Illinois. B. Jonah Lincoln lives in Springfield, Illinois. C. Sara Lucas lives in Springfield. D. Erin Naismith lives in Springfield, Massachusetts. 6. Write the two conditional statements that make up the following biconditional. I drink juice if (and only if) it is breakfast time. A. I drink juice if (and only if) it is breakfast time. It is breakfast time if (and only if) I drink juice. B. I drink juice. It is breakfast time. C. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice. D. If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time. 7. Is the following definition of dog reversible? If yes, write it as a true biconditional. A dog is a mammal. A. The reverse is false. B. The reverse is true. An animal is a dog if (and only if) it is a mammal. C. The reverse is true. An animal is a mammal if (and only if) it is a dog. D. The reverse is true. If an animal is a dog, then it is a mammal. 8. One way to show that a statement is NOT a good definition is to find a. A. converse C. biconditional B. counterexample D. conditional 9. Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides. A. A rectangle has four sides. B. A square has four congruent angles. C. A six-sided figure can have four sides congruent. D. Some triangles have all sides congruent. 10. Which statement is an example of the Addition Property of Equality? A. p = q C. If p = q then. B. If p = q then. D. If p = q then.

3 Use the given property to complete the statement. 11. Multiplication Property of Equality If, then. B. D. 12. Name the Property of Congruence that justifies the statement: If. A. Symmetric Property C. Reflexive Property B. Transitive Property D. none of these 13. Complete the two-column proof. Given: Prove: A. a. Given b. Subtraction Property of Equality c. Division Property of Equality B. a. Given b. Addition Property of Equality c. Division Property of Equality C. a. Given b. Addition Property of Equality c. Multiplication Property of Equality D. a. Given b. Subtraction Property of Equality c. Multiplication Property of Equality 14. Find Drawing not to scale A. 150 B. 20 C. 160 D What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90. A. If an angle is not a right angle, then its measure is 90. False B. If an angle is not a right angle, then its measure is not 90. True C. If an angle has a measure of 90, then it is a right angle.

4 False D. If an angle has a measure of 90, then it is a right angle. True 16. Which angles are corresponding angles? B. D. none of these 17. What is the relationship between and? m n A. alternate exterior angles C. corresponding angles B. same-side interior angles D. alternate interior angles 18. Which statement is true? A. are same-side interior angles. B. are same-side interior angles. C. are alternate angles. D. are alternate angles.

5 This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. 19. If 8 measures 127, what is the sum of the measures of 1 and 4? A. 254 B. 106 C. 127 D Which is a correct two-column proof? Given: Prove: and are supplementary. a c b d r e g f h s A.

6 B. C. D. none of these 21. Which lines are parallel if? Justify your answer. g 1 2 h j k A., by the Converse of the Same-Side Interior Angles Postulate B., by the Converse of the Alternate Interior Angles Theorem C., by the Converse of the Same-Side Interior Angles Postulate D., by the Converse of the Alternate Interior Angles Theorem 22. Each sheet of metal on a roof is perpendicular to the top line of the roof. What can you conclude about the relationship between the sheets of roofing? Justify your answer. A. The sheets of metal are all parallel to each other because in a plane, if a line is

7 perpendicular to one of two parallel lines, then it is also perpendicular to the other. B. The sheets of metal are all parallel to each other by the Alternate Interior Angles Theorem. C. The sheets of metal are all parallel to each other by the Transitive Property of Parallel Lines. D. The sheets of metal are all parallel to each other because in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. 23. If and, what do you know about the relationship between lines a and b? Justify your conclusion with a theorem or postulate. b a c A., by the Perpendicular Transversal Theorem B., by the Perpendicular Transversal Theorem C., by the Alternate Exterior Angles Theorem D. not enough information 24. Find the value of k. The diagram is not to scale k A. 42 B. 72 C. 105 D Find the value of x. The diagram is not to scale. Given:,,

8 S R T U A. 14 B. 28 C. 30 D Find the value of x. The diagram is not to scale. 110 x 57 A. 23 B. 13 C. 70 D A triangular playground has angles with measures in the ratio 8 : 6 : 4. What is the measure of the smallest angle? A. 30 B. 40 C. 5 D Which diagram suggests a correct construction of a line parallel to given line w and passing through given point K? A. B. K w

9 C. D. 29. Construct the line that is perpendicular to the given line through the given point. A. B.

10 C. D. 30. Name the angle included by the sides and N M P A. B. C. D. none of these 31. Which two triangles are congruent by ASA? N M O P Q R B. D. none

11 32. Which pair of triangles is congruent by ASA? B. D. 33. Based on the given information, what can you conclude, and why? Given: I K J H L A. by ASA C. by SAS B. by ASA D. by SAS 34. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to A. yes, by SAS; B. yes, by ASA; C. yes, by AAS; D. No, the two triangles are not congruent. 35. The octagon in the figure is equiangular and. Find.

12 A B C A. 45 B. 30 C. 135 D What common side do A B C D E F G H B. D. 37. is the bisector of and is the bisector of. Also,. Which of AAS, SSS, SAS, or ASA would you use to help you prove? A. SSS B. AAS C. SAS D. ASA 38. Which overlapping triangles are congruent by ASA?

13 B. D. Use the composition, shown below. A l C B E F D 39. Which side has an equal measure to? B. D.

14 Use the figures below. 8 y T 4 E D S R F P x X A Y 4 B Write a sequence of rigid motions that maps to. B. D. 41. Which figures are congruent? A B C D E F A. and C. B. and D. and and 42. Find the value of x.

15 14 2x 9 A. 8 B. 7 C D Find the length of the midsegment. The diagram is not to scale x x + 44 A. 42 B. 84 C. 24 D Which statement is not necessarily true? Given: is the bisector of D J K L E K is the midpoint of. B. DK = KE D. DJ = DL 45. bisects Find FG. The diagram is not to scale.

16 E n + 8 F ) 3n 4 ) D G A. 15 B. 14 C. 28 D Which diagram shows a point P an equal distance from points A, B, and C? B. D. 47. Find the circumcenter of with E(4, 4), F(4, 2), and G(8, 2). A. (3, 6) B. (4, 2) C. (6, 3) D. (4, 4) 48. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. III only B. I, II, or II C. I or III only D. I only 49. Name a median for

17 A D E ) ) C F B A. B. C. D. 50. Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. I or III only C. III only D. I, II, or II 51. has vertices Find the orthocenter of B. D. 52. Which two statements contradict each other? I. Jon, Elizabeth, and Franco read 27 books among them for a class. II. Franco read 6 books. III. None of the three students read more than 7 books. A. I and II B. I and III C. II and III D. No two of the statements contradict each other. 53. Which two statements contradict each other? I. lies on plane PQR. II. Point S lies on plane PQR. III. does not lie on plane PQR. A. I and III B. II and III C. I and II D. No two of the statements contradict each other. 54. Points B, D, and F are midpoints of the sides of The diagram is not to scale. EC = 30 and DF = 17. Find AC.

18 A F B E D C A. 34 B. 60 C. 30 D Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 150 ft A ft B ft C. 150 ft D. 75 ft 56. Where is the circumcenter of any given triangle? A. the point of concurrency of the altitudes of the triangle B. the point of concurrency of the perpendicular bisectors of the sides of the triangle C. the point of concurrency of the medians of the triangle D. the point of concurrency of the bisectors of the angles of the triangle 57. Find the length of, given that is a median of the triangle and AC = 26. D A B C A. 13 C. 26 B. 52 D. not enough information 58. In ACE, G is the centroid and BE = 18. Find BG and GE.

19 C B G D A F E B. BG = 9, GE = 9 D. 1 BG = 4 2, GE = What is the name of the segment inside the large triangle? A. angle bisector C. perpendicular bisector B. median D. altitude 60. For a triangle, list the respective names of the points of concurrency of perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes A. circumcenter incenter orthocenter centroid B. incenter circumcenter orthocenter centroid C. circumcenter incenter centroid orthocenter D. incenter circumcenter centroid orthocenter

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