Benchmark Test 1. Line Segments. Name Date. Benchmark Tests AB. Answers. Use the diagram for Exercises 1 4. Geometry.

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1 enchmark Test 1 Line Segments Use the diagram for Exercises 1 4. m A n G D l M E F Give two other names for ] A. 2. Give another name for line n. A. A ]. G ]. GE ] D. D ] 3. Name all rays with endpoint G. 4. Name the intersection of line m and the plane M. A. line m.. G D. no intersection Is it possible for three planes that are not the same to intersect in a line? 6. Use the diagram to find ST. S 34 T 13 U 7. Use the diagram to determine which pairs of line segments are congruent. A(21, 4) E(24, 3) F(23, 21) D(24, 22) y (4, 4) (4, 0) G(3,21) A. } A and } DE. } and } DE. } A and } FG D. } DE and } FG x 1

2 8. The endpoints of } A are A(7, 8) and (4, 2). a. Find the coordinates of the midpoint. b. What is the approximate length of } A? 9. The midpoint of } MN is P(5, 5). One of the endpoints is M(24, 2). Find the coordinate of endpoint N. A. (1, 7). 1 } 1 7 2, } 2 2. (14, 8) D. (7, 4) 10. What is the distance between M(6, 2) and N(4, 9)? Angles A. Ï } 81. Ï } 53. Ï } 45 D. Ï } 221 For Exercises 11 14, use the diagram to classify the angle. 8a. 8b L K F 15a. G H J 11. JHL 12. KHL 13. LHF A. acute angle. right angle. obtuse angle D. straight angle 14. GHJ A. acute angle. right angle. obtuse angle D. straight angle 15. Use the diagram shown below. P (x 1 11) (3x 1 19) O a. Name two acute angles. b. Name a right angle. c. Find the value of x. d. Find m OP and m OP. 15b. 15c. 15d. 2

3 16. S is in the interior of PRQ. If m PRQ 5 90 and m SRQ 5 37, find m SRP. 16. A D Identify the congruent angles in the diagram. 17. Q R 18. P S T 18. The measure of LOM is 53. OM ] bisects LON. lassify LON. A. acute angle. right angle. obtuse angle D. straight angle is a supplement of 2 and m Find m 1. A D A complementary pair of angles have measures (7x 1 7) and (6x 1 5). Find the measures of the two angles. 21. E A F D a. Find two pairs of vertical angles. b. Find a pair of complementary angles. c. Find three linear pairs. d. Find two angles that are adjacent to EFD. Polygons 22. Sketch an example of a convex heptagon that is not regular a. 21b. 21c. 21d. 22. See sketch. 3

4 23. A polygon has nine sides. Name the polygon. A. nonagon. hexagon. heptagon D. decagon 24. Two side lengths of a regular polygon are represented by the expressions 7x 1 8 and 13x 2 4. a. Find the value of x. b. Find the side length. 25. A rectangle has length 8 cm and width 4 cm. Find the perimeter. A. 32 cm. 12 cm. 24 cm D. 16 cm 26. Find the area and perimeter of the figure a. 24b A square has a perimeter of 44 m. What is its area? A triangle has vertices (4, 4), (3, 9) and (1, 22). Which expression gives the perimeter? A. Ï } 24 1 Ï } Ï } 27. Ï } 26 1 Ï } Ï } D. Ï } 26 1 Ï } Ï } The radius of a circle is 5 cm. Use 3.14 for. a. Find the area. b. Find the circumference. Inductive and Deductive Reasoning 30. What is the next number in the pattern? A D Here is a number pattern a. Describe the pattern. b. Write the next three numbers. 29a. 29b a. 31b. 4

5 32. Make a conjecture about the product of an odd negative integer and an even positive integer. 32. Use the following statement for Exercises The sum of two numbers is always greater than the larger number. 33. What kind of a statement is this? A. conjecture. example. inverse D. converse 34. Is the statement true or false? If false, give a counterexample. 35. Rewrite the statement in if-then form. Use the following statements for Exercises I. If the framers finish the walls on time, then the roofers finish the roof on time. II. If the roof gets put on the house on schedule, then all workers receive a bonus. III. If the framers finish the walls on time, the roofers get a bonus. 36. Write the contrapositive of the first statement. 37. Write the inverse of the third statement. 38. If the framers do not finish the walls on time, then the roofers do not finish the roof on time. This statement is a(n) of the first statement. A. contrapositive. biconditional. inverse D. converse 39. If all the workers receive a bonus, then the roof gets put on the house on schedule. This statement is a(n) of the second statement. A. contrapositive. biconditional. inverse D. converse 40. Write the definition of regular polygon as a biconditional statement. 41. Suppose the statement If it is raining then the sky is cloudy is true. y the Law of Detachment, which statement is also true? A. If the sky is cloudy today, then it is raining today.. If it is raining today, then the sky is cloudy today.. If the sky is not cloudy today, then it is not raining today. D. If it is not raining today, then the sky is not cloudy today

6 42. Apply the Law of Syllogism to write a conditional statement that follows from the pair of true statements. If Paula studies computer programming this year, then she will get a new computer. If Paula gets a new computer, then she will work for her parents. Writing Proofs 43. State the postulate illustrated by the diagram See diagram. If then Postulate 9 states A plane contains at least three noncollinear points. Make a diagram to illustrate the postulate (2x 1 8) What could be the reason for the first step in solving this equality? A. Substitution Property of Equality. Addition Property of Equality. Subtraction Property of Equality D. Division Property of Equality 46. x What could be the reason for the first step to solve this equation? 47. For any real numbers a and b, if a 5 b, then b 5 a. This is a statement of the. A. Reflexive Property of Equality. Algebraic Property of Equality. Symmetric Property of Equality D. Transitive Property of Equality 48. For any segments } RS, } ST, and } TV, if RS 5 ST and ST 5 TV then RS 5 TV. This is a statement of the. 6

7 49. Which of the following is not necessarily a part of a two-column proof? A. numbered statements. two columns. statements and postulates of logic D. a numerical answer for the unknown 50. omplete the following two-column proof. Given: K is the midpoint of } JL. IK 5 JL. I J K L Prove: J is the midpoint of } IK. Statement 1. K is the midpoint of } JL. IK 5 JL. Reasons 1. Given 2. } JK ù } KL IJ 1 JK 5 IK 3. Segment Addition Postulate JK 1 KL 5 JL 4. IJ 1 JK 5 JK 1 KL IJ 5 KL 5. Subtraction Property of Equality 6. } IJ ù } KL 6. Definition of congruent line segments 7. } IJ ù } JK J is the midpoint of } IK. 8. Definition of midpoint. 51. If m and m A 5 90, find m 2. A 2 A D Tests 7enchmark