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Guess based on an observation 3. 5. C 4x the previous number, 768

2.1 HW pg. 75-78 #1-17 odd, 22. Guess based on an observation 3. 5. C 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. 15. (1 + 2) 2 = 1 2 + 2 2 3 2 = 1 + 4

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Guess based on an observation 3. 5. C 4x the previous number, 768

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  1. 2.1 HW pg. 75-78 #1-17 odd, 22 • Guess based on an observation • 3. 5. C • 4x the previous number, 768 • 9. Subtract one more each time, –8 • 11. Add 3 more each time, 25 • 13. even

  2. 2.1 HW pg. 75-78 #1-17 odd, 22 15. (1 + 2)2 = 12 + 22 32 = 1 + 4 9  5 17. Ex. 2  5 = 10 22. B

  3. 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd • Converse • 3. If x = 6, then x2 = 36 • 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

  4. 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd • 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 • False, • 13. False, they add to 180°, but aren’t adjacent • 15. False, 2 • 16. True, measures 90°

  5. 2.2 HW pg. 82-85 1-15 odd, 16-18, 19-27 odd • 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 • Good • A • 27. If –x > –6, then x < 6. True.

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

  7. 2.3 HW pg. 90-93 #4-9, 12, 13, 16-19, 25-28 • Can’t assume because it doesn’t say hypothesis is true • You can’t buy a car • If they bakery makes a profit, you will get a raise • May have • is • True 26. True • 27. False, she buys popcorn 28. False, doesn’t say

  8. 2.4 HW pg. 99-102 #3-5, 9-13, 14-24 • If there are 2 points, then there is one line • If one plane, then 3 noncollinear points are on the plane • 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,

  9. 2.4 HW pg. 99-102 #3-5, 9-13, 14-24 • B • False, plane • true • False, parallel • true 15. false 16. false • 17. false 18. false 19. false • 20. false 21. true 22. true • 23. false • 24. C

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

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

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

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

  14. 2.6 HW pg. 116-119 #1-12, 17, 18, 21, 22, 24 • 5. • JKL  RST • J  L • Symmetric 9. Reflexive 10. Transitive • 11. Reflexive • C

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

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

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

  18. 2.7 HW pg. 127-131 #1, 8-14 even, 17-21, 23, 25, 28, 31-33, 37 • 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. True 25. False

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

  20. 37. 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 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

  21. Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20 • Theorem • ~p → ~q, q → p • mA = mC • Divide by 4, –80, –20, –5 • –1/–1 = 1 • 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°

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

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

  24. Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20 16. 3(2x + 9) = 30 Given 6x + 27 = 30 Distribution 6x = 3 Subtraction x = 0.5 Division 18. Symmetric 19. Reflexive 20. 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°

  25. Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20 • 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 • You will miss band practice • If Margot goes to college, then she will need to buy a lab manual.

  26. Ch 2 Review pg. 134-137 #1-10, 12-16, 18-20, 22, 23 pg. 138 1-5 odd, 9, 10, 17-20 • B 18. A 19. C • 20. x = 25, y = 18 126° 54° 54° 126°

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