Geometry Unit 1 Segment 3 Practice Questions

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1 Name: Class: _ Date: _ Geometry Unit 1 Segment 3 Practice Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Based on the pattern, what are the next two terms of the sequence? 9, 1, 21, 27,... a. 33, 972 b. 39, 4 c. 162, 972 d. 33, Based on the pattern, what are the next two terms of the sequence?, 3, 9, 27, 81,... a. 84, c , 246 b. 243, d , Based on the pattern, what is the next figure in the sequence? a. b. c. d. 4. Based on the pattern, make a conjecture about the sum of the first 20 positive even numbers. 2 = 2 = = 6 = = 12 = = 20 = = 30 = 6 a. The sum is c. The sum is b. The sum is d. The sum is According to the pattern, make a conjecture about the product of 13 and 8,888, = = 11, = 11, ,888 = 1,1,44 a. 11,,44 c. 1,1,,44 b. 1,11,,444 d. 11,1,, Find a counterexample to show that the conjecture is false. Conjecture: Any number that is divisible by 4 is also divisible by 8. a. 24 b. 40 c. 12 d. 26 1

2 Name: 7. Find a counterexample to show that the conjecture is false. Conjecture: The product of two positive numbers is greater than the sum of the two numbers. a. 3 and b. 2 and 2 c. A counterexample exists, but it is not shown above. d. There is no counterexample. The conjecture is true. 8. Alfred is practicing typing. The first time he tested himself, he could type 23 words per minute. After practicing for a week, he could type 26 words per minute. After two weeks he could type 29 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice. a. 39 words per minute c. 3 words per minute b. 29 words per minute d. 32 words per minute 9. May s Internet Services designs websites. May noticed an increase in her customers over a period of consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers May will have in the seventh week. 10. Find AC. a. May will have 7 customers. c. May will have 11 customers. b. May will have 9 customers. d. May will have 13 customers. a. 14 b. 1 c. 12 d If EF = 2x 12, FG = 3x 1, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale. a. x = 10, EF = 8, FG = 1 c. x = 10, EF = 32, FG = 4 b. x = 3, EF = 6, FG = 6 d. x = 3, EF = 8, FG = 1 2

3 Name: 12. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. a. x =, ST = 4 c. x = 10, ST = 60 b. x =, ST = 60 d. x = 10, ST = Which point is the midpoint of AE? a. D b. B c. not B, C, or D d. C 14. Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular. a. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles. b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. c. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles. d. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular. 1. 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. 16. Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois. a. Sara Lucas lives in Springfield. b. Jonah Lincoln lives in Springfield, Illinois. c. Billy Jones lives in Chicago, Illinois. d. Erin Naismith lives in Springfield, Massachusetts. 3

4 Name: 17. Draw a Draw a Venn diagram to illustrate this conditional: Cars are motor vehicles. a. c. b. d. 18. 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; conclusion b. hypothesis; conclusion; conditional d. hypothesis; conditional; conclusion 19. A conditional can have a of true or false. a. hypothesis b. truth value c. counterexample d. conclusion 20. 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. If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday. d. Yesterday was Tuesday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday. 4

5 Name: 21. What is the conclusion of the following conditional? A number is divisible by 3 if the sum of the digits of the number is divisible by 3. a. The number is odd. b. The sum of the digits of the number is divisible by 3. c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. d. The number is divisible by What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. a. If a point is in the first quadrant, then its coordinates are positive. b. If a point is not in the first quadrant, then the coordinates of the point are not positive. c. If the coordinates of a point are positive, then the point is in the first quadrant. d. If the coordinates of a point are not positive, then the point is not in the first quadrant. 23. 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 measure 90, then it is a right angle. False d. If an angle has measure 90, then it is a right angle. True 24. Which conditional has the same truth value as its converse? a. If x = 7, then x = 7. b. If a figure is a square, then it has four sides. c. If x 17 = 4, then x = 21. d. If an angle has measure 80, then it is acute. 2. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 3, then x 2 = 9. a. If x 2 = 9, then x = 3. True; x 2 = 9 if and only if x = 3. b. If x 2 = 3, then x = 9. False c. If x 2 = 9, then x = 3. True; x = 3 if and only if x 2 = 9. d. If x 2 = 9, then x = 3. False 26. 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 two lines are parallel, they do not intersect. If two lines do not intersect, they are parallel. a. One statement is false. If two lines do not intersect, they could be skew.. b. One statement is false. If two lines are parallel, they may intersect twice. c. Both statements are true. Two lines are parallel if and only if they do not intersect. d. Both statements are true. Two lines are not parallel if and only if they do not intersect.

6 Name: 27. 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. 28. 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. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice. c. If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time. d. I drink juice. It is breakfast time. 29. When a conditional and its converse are true, you can combine them as a true. a. counterexample c. unconditional b. biconditional d. hypothesis 30. Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are congruent, then they have equal measures. P and Q are congruent. a. m P + m Q = 90 c. P is the complement of Q. b. m P = m Q d. m P m Q 31. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. I can go to the concert if I can afford to buy a ticket. I can go to the concert. a. I can afford to buy a ticket. b. I cannot afford to buy the ticket. c. If I can go to the concert, I can afford the ticket. d. not possible 32. Which statement is the Law of Detachment? a. If p q is a true statement and q is true, then p is true. b. If p q is a true statement and q is true, then q p is true. c. If p q and q r are true, then p r is a true statement. d. If p q is a true statement and p is true, then q is true. 6

7 Name: 33. 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 3x 4 =. Statement 2: x = 3 a. 3x 4 = c. If 3x 4 =, then x = 3. b. x = 3 d. not possible 34. Use the Law of Syllogism to draw a conclusion from the two given statements. If a number is a multiple of 64,then it is a multiple of 8. If a number is a multiple of 8, then it is a multiple of 2. a. If a number is a multiple of 64, then it is a multiple of 2. b. The number is a multiple of 2. c. The number is a multiple of 8. d. If a number is not a multiple of 2, then the number is not a multiple of Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If an elephant weighs more than 2,000 pounds, then it weighs more than Jill s car. If something weighs more than Jill s car, then it is too heavy for the bridge. Smiley the Elephant weighs 2,10 pounds. a. Smiley is too heavy for the bridge. b. Smiley weighs more than Jill s car. c. If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge. d. If Smiley weighs more than Jill s car, then Smiley is too heavy for the bridge. 36. Which statement is the Law of Syllogism? a. If p q is a true statement and p is true, then q is true. b. If p q is a true statement and q is true, then p is true. c. if p q and q r are true statements, then p r is a true statement. d. If p q and q r are true statements, then r p is a true statement. 7

8 Name: Fill in each missing reason. 37. Given: m PQR = x, m SQR = x 11, and m PQS = 100. Find x. m PQR + m SQR = m PQS x + x 11 = 100 2x 16 = 100 2x = 116 x = 8 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 8

9 Name: 38. Given: 11x 6y = 1; x = 8 Prove: 89 6 = y 11x 6y = 1; x = 8 a. 88 6y = 1 b. 6y = 89 y = c. d. = y e. a. a. Given b. Symmetric Property of Equality c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality b. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Symmetric Property of Equality c. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality d. a. Given b. Substitution Property c. Subtraction Property of Equality d. Addition Property of Equality e. Symmetric Property of Equality 39. Name the Property of Equality that justifies the statement: If p = q, then p r = q r. a. Reflexive Property c. Symmetric Property b. Multiplication Property d. Subtraction Property 40. Which statement is an example of the Addition Property of Equality? a. If p = q then p s = q s c. If p = q then p s = q s b. If p = q then p + s = q + s. d. p = q 41. Name the Property of Congruence that justifies the statement: If XY WX, then WX XY. a. Symmetric Property c. Reflexive Property b. Transitive Property d. none of these 42. Name the Property of Congruence that justifies the statement: If A B and B C, then A C. a. Transitive Property c. Reflexive Property b. Symmetric Property d. none of these 9

10 Name: Use the given property to complete the statement. 43. Transitive Property of Congruence If CD EF and EF GH, then. a. EF GH c. CD GH b. EF EF d. CD EF 44. Multiplication Property of Equality If 4x 2 = 4, then. a. 4 = 4x 2 c. 4x = 8 b. 4 = 4x 2 d. 4x 2 = 8 4. Substitution Property of Equality If y = 3 and 8x + y = 12, then. a. 8(3) y = 12 c. 8x + 3 = 12 b. 3 y = 12 d. 8x 3 = BD bisects ABC. m ABC = 7x. m ABD = 3x + 2. Find m DBC. a. 0 b. 12 c. 7 d Find the value of x. a. 19 b. 12 c. 19 d. 48. m 3 = 37. Find m 1. a. 37 b. 143 c. 27 d

11 Name: 49. What is the negation of this statement? Miguel s team won the game. a. It was not Miguel s team that won the game. b. Miguel s team lost the game. c. Miguel s team did not win the game. d. Miguel s team did not play the game. 0. What is the inverse of this statement? If he speaks Arabic, he can act as the interpreter. a. If he does not speak Arabic, he can act as the interpreter. b. If he speaks Arabic, he can t act as the interpreter. c. If he can act as the interpreter, then he does not speak Arabic. d. If he does not speak Arabic, he can t act as the interpreter. 1. Write the conditional statement illustrated by this Venn diagram. a. If an animal is a mammal, then it is a cow. b. If an animal is a cow, then it is a mammal. c. If an animal is a mammal, then it is not a cow. d. If an animal is a cow, then it is not a mammal. 2. Write the contrapositive of the conditional statement illustrated by this Venn diagram. a. If an animal is not a poodle, then it is a dog. b. If an animal is not a dog, then it is a poodle. c. If an animal is not a poodle, then it is not a dog. d. If an animal is not a dog, then it is not a poodle. 11