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Transcript

Year 2 Chapter 2 Review 1. Reasoning based on facts. Reasoning based on observation and assumptions a. b. c. d. Inductive, inductive Inductive, deductive Deductive, deductive Deductive, inductive 4. Find a and b. a 133˚ 58˚ a. b. c. d. b a 58, b 133 a 122, b 47 a 58, b 47 a 122, b 133 2. Which pair of angles are a linear pair? A 5. Solve for x. F G B (4 x 60) E (3 x 43) D C BGD and FGD BGA and CGD CAB and AGE BGA and AGE a. b. c. d. a. b. c. d. x 35 x 30 x 15 x 11 3. Which pair of angles are a vertical pair? A F G B 6. Solve for x. E (8 x 70) D C a. b. c. d. CGD and AGF DGE and AGC AGF and FGE CGE and CGD (3 x 25) a. b. c. d. x 35 x 30 x2 x 9 7. Find the missing elements in the sequence below: -7, 14, -28, 56, -112, 224, _______, 896, -1792, _______, -7168, … 8. What is conclusion can you make? If triangle ABC is an isosceles, then it has two congruent sides. If it has two congruent sides, then it has a pair of congruent angles. Therefore, if triangle ABC is an isosceles, then _______________________. A) it is a scalene. B) it has three congruent sides. C) it has a pair of congruent angles. D) it has three congruent angles. 9. Write the measure of all the missing angles. 11. Find the measure of p c a 67 b 22 90 10. A) State the type of angles. B) State the relationship C) Solve for x. D) Find A and B. (9x – 43)=A p 12. Teresa drew 10 sets of parallel lines and drew a transversal through each. She measured each set and found that there was always one obtuse and one acute angle. A) What reasoning did she use to make the statement, "Parallel lines with one transversal have one obtuse and one acute angle"? (4x + 17)=B B) Is the reasoning valid? If not, construct a counterexample. 13. Use the following statement to answer numbers i-iii. If a triangle has three different sides, then it is a scalene triangle. A) If a triangle is a scalene, then it has three different sides. B) If a triangle has three different sides, then it is not a scalene triangle. C) If a triangle does not have three different sides, then it is not a scalene triangle. D) If a triangle is not a scalene triangle, then it does not have three different sides. i. Which is the converse of the statement? _____________ ii. Which is the inverse of the statement? _____________ iii. Which is the contrapositive of the statement? _____________ 14. Use your parallel line conjectures to determine what is wrong with this picture. l 87 88 m Use the following diagram to answer 15-17. 1 2 3 4 5 6 7 8 15) Name a pair of corresponding angles. a. 1, 5 b. 6, 4 c. 3, 6 d. 2, 7 16) Name a pair of alternate interior angles. a. 1, 5 b. 6, 4 c. 3, 6 d. 2, 7 17) Name a pair of alternate exterior angles. a. 1, 5 b. 6, 4 c. 3, 6 d. 2, 7 18. Which of the following is not a Euclid Postulate? A) Any line segment can be extended indefinitely in a ray. B) All right angles are congruent. C) If l is any line and P is any point not on l, then there exists one line through P that is parallel to l. D) Given a line segment, a circle can be drawn having the segment as a radius and one endpoint as a center. 19. Find the measure of each lettered angle in the figure. a = ________, b = ________ c = ________, d = ________ e = ________, f = ________ g h 142o a d g = ________, h = ________ 106o b c f e 130o 20. Draw the next shape in the pattern. 21. If <A and <B are complementary and <A and <C are congruent. What relationship do <B and <C have? Use deductive reasoning to fill in the two column proof. Statement Reason 1. 1. A and B are complementary. 2. 2. Given 3. A B 90 3. 4. 4. Substitution 5. 5. Definition of Complementary. 22. Solve the following problem algebraically. Make sure you give reasons for each step. Statement 1. 2(x + 1) – 5x + 4 = 3(x – 30) 2. Reason 1. Given 2. Distributive Property 3. 3. 4. 4. Subtraction Property 5. 5. 6. 6. **Extra Credit**_______________________________________________________________________ Solve for x. 23. x 7 5 9 24. 3 5x 9 6 26. 3x 6 24 27. 2 x 4 5 x 3 4 8 25. 6 x 2 16 200 28. 28. Solve for b: y mx b