1. 1.Guess based on an observation 3. 5. C 7.4x the previous number, 768 9. Subtract one more each time, –8 11. Add 3 more each time, 25 13. even 2.1 HW pg. 75-78 #1-17 odd, 22

2. 15. (1 + 2) 2 = 1 2 + 2 2 3 2 = 1 + 4 9  5 17. Ex. 2  5 = 10 22. B 2.1 HW pg. 75-78 #1-17 odd, 22

3. 1.Converse 3. If x = 6, then x 2 = 36 5.If a person is registered, then they are allowed to vote 7. If two angles are complementary, then they add to 90° Con: If two angles add to 90°, then they are complementary Inv: If two angles aren’t complementary, then they don’t add to 90° Cont: It two angles don’t add to 90°, then they aren’t complementary 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd

4. 9. If 3x + 10 = 16, then x = 2 Con: If x = 2, then 3x + 10 = 16 Inv: If 3x + 10  16, then x  2 Contr: If x  2, then 3x + 10  16 11. False, 13. False, they add to 180°, but aren’t adjacent 15. False, 2 16. True, measures 90° 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd

5. 17. m  1 = 90° 18.  2 &  3 are a linear pair 19. An angle measures between 90° and 180° iff it is obtuse 21. Points are coplanar iff they lie on the same plane 23. Good 25. A 27. If –x > –6, then x < 6. True. 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd

6. 4.Then it is a right angle 5. –15 < –12 6.It is nonfiction 7.If a rectangle has 4 equal side lenghts, then it is a regular polygon. 8.If y > 0, then 2y – 5  –5 9.If you play the clarinet, then you are a musician 12. B 2.3 HW pg. 90-93 #4-9, 12, 13, 16-19, 25-28

7. 13. Can’t assume because it doesn’t say hypothesis is true 16. You can’t buy a car 17. If they bakery makes a profit, you will get a raise 18. May have 19. is 25. True26. True 27. False, she buys popcorn28. False, doesn’t say 2.3 HW pg. 90-93 #4-9, 12, 13, 16-19, 25-28

8. 3.If there are 2 points, then there is one line 4.If one plane, then 3 noncollinear points are on the plane 5.If 3 points are noncollinear, then there is a plane. Con: If there is a plane, then there are 3 noncollinear points Inv: If there isn’t a plane, then there isn’t 3 noncollinear pts Cont: If there isn’t 3 noncollinear pts, then there isn’t a plane 9. No, 2.4 HW pg. 99-102 #3-5, 9-13, 14-24

9. 10.B 11. False, plane 12. true 13. False, parallel 14. true15. false16. false 17. false18. false19. false 20. false21. true22. true 23. false 24. C 2.4 HW pg. 99-102 #3-5, 9-13, 14-24

10. 1.Reflexive 2.Subtraction, addition, division 4.Distributive, subtraction, addition 5.D 7.4x + 9 = 16 – 3xGiven 7x + 9 = 16Addition 7x = 7Subtraction x = 1Division 2.5 HW pg. 108-111 #1, 3-5, 7, 9, 17, 21-26, 41, 42

11. 9.3(2x + 11) = 9Given 6x + 33 = 9Distribution 6x = –24Subtraction x = –4Division 17. 12 – 3y = 30xGiven –3y = 30x – 12 Subtraction y = –10x + 4Division 21. 20 + CD 22. m  2 = m  1 23. AB + EF = CD + EF 2.5 HW pg. 108-111 #1, 3-5, 7, 9, 17, 21-26, 41, 42

12. 24. 5x + 40 = 2 25. m  1 = m  3 26. 7x = x + 24Given 6x = 24Subtraction x = 4Division 41. Ex. 42. is 2.5 HW pg. 108-111 #1, 3-5, 7, 9, 17, 21-26, 41, 42

13. 1.Statement that is proved 2.Definitions, postulates, properties 3. AB = 5, BC = 6Given AC = AB + BCSegment Addition AC = 5 + 6Substitution AC = 11Simplify 4. m  1 = 59°, m  2 = 59°Given 59° = m  2 Symmetric Property m  1 = m  2 Transitive Property 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24

14. 5. 6.  JKL   RST 7.  J   L 8.Symmetric9. Reflexive10. Transitive 11. Reflexive 12. C 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24

15. 17. Given Transitive Property 2x + 5 = 10 – 3xSubstitution 5x + 5 = 10Addition 5x = 5Subtraction x = 1Division 18. m  ABC = 90°Given m  ABD + m  DBC = 90°Angle Addition Postulate 6x + 3x – 9 = 90Substitution 9x – 9 = 90Simplify 9x = 99Addition x = 11Division 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24

16. 21. bisects  UTWGiven  1   2Def. of angle bisector  2   3Given  1   3Transitive 22. bisects  PQRGiven (D)  PQS   SQRDef. of angle bisector (A) m  PQS = m  SQRDef of congruent angles (F) m  PQS + m  SQR = m  PQRAngle addition (C) m  PQS + m  PQS = m  PQRsubstitution (G) 2(m  PQS) = m  PQRDistributive (B) m  PQS = ½(m  PQR)Division (E) 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24

17. 24. m  1 + m  2 = 180° Given m  1 = 62°Given 62 + m  2 = 180° Substitution m  2 = 118° Subtraction 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24

18. 1. vertical 8. m  1 = 145°, m  2 = 35°, m  3 = 145°, m  4 = 35° 10. m  1 = 143°, m  2 = 37°, m  3 = 143°, m  4 = 37° 12. x = 11, y = 17 14. x = 4, y = 9 17. 30°18. 25°19. 27° 20. 133°21. 58° 23. True25. False 2.7 HW pg. 127-131 #1, 8-14 even, 17-21, 23, 25, 28, 31-33, 37

19. 28. x = 18, y = 13 m  1 = 130°, m  2 = 50°, m  3 = 130°, m  4 = 50° 31.  EGH   FGH by the definition of angle bisector 32.  1   9 by the congruent complements theorem 33.  AEC   CEB   BED   AED, def of perp. Lines 2.7 HW pg. 127-131 #1, 8-14 even, 17-21, 23, 25, 28, 31-33, 37

20. 1.  1 &  2 are complementary 1. Given  1 &  3 are complementary 2. m  1 + m  2 = 90°, m  1 + m  3 = 90° 2. Def. of comp. angles 3. m  1 + m  2 = m  1 + m  3 3. Transitive Prop. 4. m  2 = m  3 4. Subtraction 5.  2   3 5. Def. of  angles 37.

21. 1. Theorem 2. ~p → ~q, q → p 3. m  A = m  C 4. Divide by 4, –80, –20, –5 5. –1/–1 = 1 6. If an angle measures 34°, then it is acute. Con: If an angle is acute, then it measures 34° Inv: If an angle doesn’t measure 34°, then it isn’t acute Cont: If an angle isn’t acute, then it doesn’t measure 34° Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20

22. 7. Yes, def. of complementary angles 8. A polygon is equiangluar iff all of its angles are congruent 9. It measures 90° 10. If 4x = 12, then 2x =6. 12. Ex. 13. B Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20

23. 14. –9x – 21 = –20x – 87 Given 11x – 21 = –87 Addition 11x = 66Addition x = 1Division 15. 15x + 22 = 7x +62 Given 8x + 22 = 62Subtraction 8x = 40Subtraction x = 5Division Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20

24. 16. 3(2x + 9) = 30Given 6x + 27 = 30Distribution 6x = 3Subtraction x = 0.5Division 18. Symmetric19. Reflexive20. Transitive 22. m  1 = 114°, m  2 = 66°, m  3 = 114°, m  4 = 66° 23. m  1 = 123°, m  2 = 57°, m  3 = 123°, m  4 = 57° Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20

25. 1. 3. Add 5, 14 5. If 2 angles are right angles, then they are congruent Con: If two angles are congruent, then they are right angles Inv: If 2 angles aren’t right angles, then they aren’t congruent Cont: If 2 angles aren’t congruent, then they aren’t right angles 9. You will miss band practice 10. If Margot goes to college, then she will need to buy a lab manual. Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20

26. 17. B18. A19. C 20. x = 25, y = 18 Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20 126° 54°