HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question.
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1 Geometry Homework Worksheets: Chapter 2 HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question. 1. Which of the following statements is/are always true? I. adjacent angles are acute II. if m270, then 2 is acute III. two acute angles make a right angle A. I only B. II only C. III only D. both I and II E. I, II, and III 3. Identify a counterexample to the given statement: If A is obtuse, then ma120 A. A is an acute angle B. A is a right angle C. ma120 D. ma80 E. ma Identify the converse of the conditional statement below: If I break my ipod, I will get in trouble. A. If I don t break my ipod, I won t get in trouble. B. If I break my ipod, I will get in trouble. C. If I get in trouble, I will break my ipod. D. If I don t get in trouble, I didn t break my ipod. E. none of the above 4. All of the following statements are true except: A. Opposite rays share an endpoint. B. The intersection of two planes is a point. C. Four non-coplanar points determine space. D. Obtuse angles measure more than 90 degrees. E. Congruent segments have the same length. For questions 5-8 translate each of the following into a mathematical expression. 5. The difference of four times a number and seven. 6. Three times the difference of a number and two. 7. The sum of two and the quotient of a number and five. 8. The product of four times a number and nine.
2 HW Set #2 (Problems 9-15) For #9-12, choose the best answer for each multiple choice question. 9. If A and B are supplementary angles, what angle relationship between A and B CANNOT be true? (A) A and B are right angles (B) A and B are adjacent angles (C) A and B are complementary angles (D) A and B are congruent angles 11. What value of x is a counterexample to the statement below? If x 2 8 0, then x 3. (A) 4 (B) 2 (C) -2 (D) Which number is a counterexample to the statement below? All prime numbers are odd. (A) 0 (B) 2 (C) 34 (D) Which statement is NOT true? (A) If two lines are parallel, then they lie in one plane and do not intersect. (B) Two lines lie in one plane if and only if the lines are parallel. (C) If two coplanar lines do not intersect, then the lines are parallel. (D) Two lines lie in one plane and do not intersect if and only if the two lines are parallel. For questions 13-14, solve each equation. If necessary, leave your answers as reduced fractions x 1 5 x x x For questions translate each of the following into a mathematical expression. 15. Seven less than twice a number 16. Eight more than the quotient of seven and x.
3 HW Set #3: Problems #16-22 For #16-22, choose the best answer for each multiple choice question. 16. The following statement is an example of which property: 2 If x, then 2x A. Addition Property of Equality C. Multiplication Property of Equality D. Division Property of Equality E. Distributive Property of Equality 17. The following statement is an example of which property? -11xy + 2x 2 = 11xy + 2x 2 A. Transitive Property of Equality B. Symmetric Property of Equality C. Reflexive Property of Equality D. Substitution Property of Equality E. Distributive Property of Equality Choose the best answer for each multiple choice question. For #18-22, you are completing a proof. Given: 5(2x 6) = 4x + 6 Prove: x = 6 5(2x 6) = 4x x 30 = 4x + 6 #20 6x = 36 x = What reason should be written in the space marked #18 of this proof? A. Given C. Distributive Property of Equality E. Reflexive Property 20. What statement should be written in the space marked #20 of this proof? A. 10x = 4x + 36 B. 6x = 36 C. 6x 30 = 6 D. None of these 22. What reason should be written in the space marked #22 of this proof? Reasons #18 #19 Subtraction Property of Equality #21 # What reason should be written in the space marked #19 of this proof? A. Substitution Property of Equality C. Distributive Property of Equality E. Reflexive Property 21. What reason should be written in the space marked #21 of this proof? A. Substitution Property of Equality C. Distributive Property of Equality E. Reflexive Property A. Subtraction Property of Equality B. Division Property of Equality C. Prove E. Multiplication Property of Equality
4 HW Set #4: Problems #23-28 For #23-26, choose the best answer for each multiple choice question. Choose the best answer for each multiple choice question. For #23-26, you are completing a proof. Given: AB = XY, BC = YZ Prove: AC = XZ Statements AB = XY BC = YZ AB + BC = XY + YZ AC = AB + BC XZ = XY + YZ # What reason should be written in the space marked #23 of this proof? A. Substitution Property of Equality C. Segment Addition Postulate E. Definition of Midpoint 25. What statement should be written in the space marked #25 of this proof? Reasons Given #23 #24 # What reason should be written in the space marked #24 of this proof? A. Addition Property of Equality C. Segment Addition Postulate D. Definition of Midpoint E. Transitive Property of Equality 26. What reason should be written in the space marked #26 of this proof? A. AB = XY, BC = YZ B. AC = XZ C. AC + XZ = AB + XY + BC + YZ D. B is the midpoint of AC E. Y is the midpoint of XZ A. Prove B. Addition Property of Equality C. Subtraction Property of Equality D. Substitution Property of Equality E. Segment Addition Postulate For questions 27-28, fill in the reasons for each of the given statements. 27. Given: RT = SU and the figure at the right. Prove: RS = TU RT = SU ST = ST RT ST = SU ST RT ST = RS SU ST = TU RS = TU 28. Given: M is the midpoint of AB Prove: 2AM AB M is the midpoint of AB AM MB AM = MB AM + MB = AB AM + AM = AB 2AM AB
5 HW#5: Problems #29-34 For questions 29-32, complete the two column proof for each situation. 29. Given: M is the midpoint of AB N is the midpoint of CD AB = CD Prove: AM = CN AM + AM = CN + CN 2AM = 2CN 7.) 30. Given: QS is an angle bisector of 1 Prove: mpqs m 2 mpqs m SQR mpqsmsqrm mpqsmpqs m 2mPQS m 1 mpqs m 2 Def. of midpoint SAP Substitution prop. of equality 7). 31. Given: RT = 5, RS = 5, RT TS Prove: RS TS RT = RS Def. of congruent segments MORE ON THE NEXT PAGE!!
6 32. Given: 1 and 2 are complements 1 and 3 are complements Prove: 2 3 m1m2m1m 3 m1 m 1 Def. of complementary angles Subtraction prop. of equality For questions 33-34, set up an equation & solve to find the unknown angle measurement. 33. The sum of an angle, its complement, and its supplement is 200. Find the angle 34. The sum of an angle, its complement, and four times its supplement is 690.
7 HW#6: Problems #35-49 For questions 35-38, simplify each expression as much as possible. If necessary, leave your answers as reduced fractions For questions 39-40, find the midpoint of the segment with the given endpoints. 39. (-8, 9) and (-2, -6) 40. (7, -5) and (-9, -13) For questions 41-44, solve each equation. If necessary, leave your answers as reduced fractions ( 3r2) ( r 1) y 5 y x x x 6x7 45. Find the missing endpoint of HG if H has coordinates (5, -2) and the midpoint of HG is (-4, 8).
8 For questions 46-49, find the value of the variable(s) x (7x+37) (5x-10) 3y (4x+4) (5y-80) 48. m LMN P L (11x-9) (5x+5) M N (2x+2) (x+1)
*Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper*
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