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Reflexive Property <1 = <1 or AB = AB X  Vertical Angles <1 = <2

Reflexive Property <1 = <1 or AB = AB X  Vertical Angles <1 = <2. 3. T  Supplementary Angles <1 + <2 = 180. 4. || lines and Converses for proving || lines. Z Alternate Int. <1 = <2 F Corresponding <1 = <2 U Same Side Int. <1 + <2 = 180. 5. Triangle Angles

jeremy-fitzgerald
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Reflexive Property <1 = <1 or AB = AB X  Vertical Angles <1 = <2

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  1. Reflexive Property <1 = <1 or AB = AB • X  Vertical Angles <1 = <2 3. T  Supplementary Angles <1 + <2 = 180 4. || lines and Converses for proving || lines • Z Alternate Int. <1 = <2 • F Corresponding <1 = <2 • U Same Side Int. <1 + <2 = 180 • 5. Triangle Angles • Int <1 +<2 +<3 + 180 • Ext <1 +<2 +<3 = 360 • 2 Int. = Ops Ext <1 + <2 = <3

  2. 6. Polygons • Int Angles I = (n-2)180 • Ext. Angles E = 360 • Int/Ext. I1+ E1 = 180 • 7. Proving Triangles Congruent • SSS • SAS A is Included Angle • ASA S is Included Side • AAS S is not an Included Side • RHL

  3. 8. Isosceles Triangles • S1 = S2  Opp <1 = <2 • <1 = <2  Opp S1 = S2 • Equilateral triangles have all 60° angles • 9. Triangle Implieds • Median of Tri  bisected base S1 = S2 • Altitude of Tri  perpendicular to base • Perpendicular Bisector  median and alt. • Points on bisectors  D1 = D2

  4. 10. Parallelograms • 2 Pair of opposite sides parallel • 2 Pair of opposite sides equal • 2 Pair of opposite angles equal • Diagonals bisect each other • 11. Proving parallelograms. • Converse of above four , plus • Show one pair of sides || and =

  5. 12. a) Three or More Parallel Lines with b) One Transversal cut into equal parts. •  The other transversal cut into equal parts. • 13. a) One transversal cut into equal parts b) a second transversal cut into equal parts •  The lines doing the cutting are parallel. • 14. and M = ½ B

  6. 15. and M = ½ B • 16. Rectangles are the opposite of Rhombuses • Diagonals of a Rectangle • Form 4 equal center segments • Diagonals of a Rhombus • Form 4 equal center angles • And bisect the corner angles. (equal angles) (equal sides)

  7. A 1 2 B Given: <1 = <2 Answer: No Conclusion because Same side int. angles aren’t 180

  8. 1 A 2 B Given: <1 = <2 Answer: It follows A||B Corresponding Angles are cong.  ||

  9. A 1 2 B Given: <1 + <2 = 180 Answer: No Conclusion because Alternate int. angles aren’t cong.

  10. 1 A 2 B Given: <1 + <2 = 180 Answer: No Conclusion because Coresponding angles aren’t cong.

  11. A 1 2 B Given: <1 + <2 = 180 Answer: It follows A||B Same side int. angles are 180  ||

  12. A 1 2 B Given: A||B Answer: It follows that <1 = <2 ||  Alternate int. angles are cong.

  13. 1 A 2 B Given: A||B Answer: It follows that <1 = <2 ||  Corresponding angles are cong.

  14. A 1 2 B Given: <1 = <2 Answer: It follows A||B Alternate int. angles are cong.  ||

  15. A 1 2 B Given: A||B Answer: It follows that <1 + <2 = 180 ||  Same side int. angles are 180.

  16. 1 2 3 What can you say? Answer: <1 + <2 = <3 2 Interior <‘s = Ops exterior

  17. 1 3 2 What can you say? Answer: <1 + <2 + <3 = 180 Interior angles

  18. 1 2 3 What can you say? Answer: <1 + <2 + <3 = 360 Exterior angles

  19. I What can you say? Answer: I = (N-2)180 Interior angles

  20. E What can you say? Answer: E = 360 Exterior angles

  21. E1 I1 What can you say? Answer: E = 360 Exterior angles

  22. C F 1 A 2 D 3 6 B 4 5 H Answer: Reflexive Prop. G E

  23. C F 1 A 2 D 3 6 B 4 5 H G E

  24. C F 1 A 2 D ⟘ 3 6 B ⟘ 4 5 H G E ⟘

  25. C F 1 A 2 D 3 6 B 4 5 H Answer: Def. of < Bisector G E

  26. C F 1 A 2 D 3 6 B 4 5 H G E

  27. C F 1 A 2 D Question: If <ADF and <4 are supplements, then m<ADF + m<4 = 180 3 6 B 4 5 H G Answer: Def. of Supplementary Angles E

  28. C F 1 A 2 D Question: AD + DB = AB 3 6 B 4 5 H Answer: Seg. Add. Post. G E

  29. C F 1 A 2 D Question: m<1 +m<2 = m<CDB 3 6 B 4 5 H Answer: Ang. Add. Post. G E

  30. C F 1 A 2 D Question: If D is the midpoint of AB, then AD = ½ AB . 3 6 B 4 5 H Answer: Midpt. Thm. G E

  31. C F 1 A 2 D Question: If m<ADF + m<FDB = 180 3 6 B 4 5 H Answer: Def. of Supp. Angles G E

  32. C F 1 A 2 D 3 6 B 4 5 H Answer: Def. Rt. Angle G E

  33. C F 1 A 2 D 3 6 B 4 5 H Answer: Def. of Angle Bisector G E

  34. C F 1 A 2 D Question: If m<3 + m<4 = 90, then <3 and <4 are complements. 3 6 B 4 5 H G Answer: Def. of Complementary Angles E

  35. C F 1 A 2 D 3 6 B 4 5 H G E

  36. C F 1 A 2 D 3 6 B 4 5 H G E

  37. C F 1 A 2 D Question: If RS = TW, then TW = RS 3 6 B 4 5 H Answer: Symmetric Prop. G E

  38. C F 1 A 2 D Question: If 5y = -20, then y = -4 3 6 B 4 5 H Answer: Div. Prop. Of = G E

  39. C F 1 A 2 D Question: 2(a + b) = 2a + 2b 3 6 B 4 5 H Answer: Distributive Prop. Of = G E

  40. C F 1 A 2 D Question: 2x + y = 70 and y = 3x, then 2x + 3x = 70 3 6 B 4 5 H Answer: Substitution Prop. G E

  41. C F 1 A 2 D Question: If AD = DB and DB = DC, and DC = 23 then AD = 23. 3 6 B 4 5 H Answer: Transitive Prop. G E

  42. C F 1 A 2 D Question: If x + 5 = 16, then x = 11. 3 6 B 4 5 H Answer: Subtraction Prop. Of = G E

  43. C F 1 A 2 D 3 6 B 4 5 H Answer: Multiplication Prop. of =. G E

  44. C F 1 A 2 D 3 6 B 4 5 H Answer: Transitive Prop. of =. G E

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