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Math Properties & Proofs Guide

Learn essential math properties of equality, definitions of congruence and midpoint, angle bisector theorems, and how to use them in proofs. Understand VAT, EST, SAT, CAT, and angle relationships.

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Math Properties & Proofs Guide

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  1. 2.2 Proof Properties Memorize these ASAP!

  2. Properties of Equality Addition Property of Equality: _________________________________ Subtraction Property of Equality: ________________________________ Multiplication Prop. of Equality: ________________________________

  3. Division Property of Equality: ________________________________ Substitution Property of Equality: _______________________________ Reflexive Prop. of Equality: _______________________________ Symetric Prop. of Equality: _______________________________

  4. Transitive Property of Equality: _________________________________ Definition of Congruence: ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________

  5. Definition of a Midpoint: ______________________________________ Midpoint Theorem: ________________________________________________ ________________________________________________ ________________________________________________ A X B

  6. Definition of Angle Bisector: ______________________________________ Angle Bisector Theorem: ______________________________________________ ______________________________________________ A Y B C

  7. Vertal Angle Theorem (VAT): Segment Addition Postulate (SAP): Angle Addition Postulate (AAP): 1 2 A B C A D B C

  8. Proof- ____________________________ __________________________________ We will now use all the theorems, postulates and properties we just defined to solve proofs. Lets try a Algebra Proof first.

  9. Given: 4x+3 = 2x -9 Prove: x= -6 Given always first statement and reason! Statements Reasons

  10. A B C D E F

  11. A B C D

  12. A B C D

  13. Have we noticed a pattern? • Parts to Whole (given pieces, asked to prove whole) • ______________________________________ • ______________________________________ • ______________________________________ • Whole to Parts (given Whole, asked to prove parts) • ______________________________________ • ______________________________________ • ______________________________________

  14. 2.2 Proofs Continued

  15. K G H J K

  16. E F H G

  17. A B C D E F

  18. S Q P 3 4 1 2 R T

  19. S Q P Z 3 4 1 2 R T

  20. S Q P Z 3 4 1 2 R T

  21. S Q P Z 3 4 1 2 R T

  22. 3 1 2

  23. C B D 3 1 2 4 A E F

  24. 2.4 Vertical Angle Theorem

  25. Lets Prove VAT 3 1 2

  26. VAT- ___________________________ ________________________________________________________________________________________________ Supplement and Complement:

  27. Complete with Always, Sometimes or Never • Vertical angles____________ have a common vertex? • 2 right angles are _________complementary. • Right angles are _________ vertical angles. • Vertical angles___________ have a common supplement.

  28. Lets Prove VAT 1 2 3 4

  29. 2.5 Perpendicular Lines

  30. Definition of Perpendicular Lines: • _____________________________________________________________________ • ________________________________________________________________________________________________________

  31. Theorem 2-4:___________________________ ____________________________________________________________________________ s 1 2 t

  32. Definition of Complementary Angles ________________________________________ ________________________________________ Definition of Supplementary Angles _________________________________________ _________________________________________ _________________________________________

  33. Exterior Sides Theorem (EST): ___________________________________________________________________________________________________________________________ S 2 1 T ___________________________________________________________________________________________________________________________

  34. E C A G • True or False: • Angle CGB is a right angle? • Angle CGA is a right angle? • Angle DGB is 90 degrees? • EGC and EGA are compliments? • DGF is complementary to DGA? • EGA is complementary to DGF B D F

  35. 2.6 SAT and CAT

  36. Supplementary Angle Theorem (SAT) ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ Example: If 1 is supp to 2 and 2 is sup to 3 Then SAT says

  37. Complementary Angle Theorem (CAT) ____________________________________________________________________________________________________________________________________________________________________________________ Example: If 1 is comp to 2 and 2 is comp to 3 Then CAT says

  38. When to use? • ___________________________________________________________________________________ • ___________________________________________________________________________________ • ___________________________________________________________________________________ • ___________________________________________________________________________________

  39. 1 2 4 3

  40. 3 4 1 2

  41. 2 1 3 4

  42. A 3 2 1 C B

  43. 1 2 3 4

  44. 1 2 3 4

  45. 1 2 3 4

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