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2-2 Properties from Algebra

2-2 Properties from Algebra. Notes on worksheet. Properties from Algebra. See Worksheet! Addition Property Subtraction Property Multiplication Property Division Property. You can +/-/x/÷ the same number on both sides of an equation. Properties from Algebra. Substitution: think “replace”

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2-2 Properties from Algebra

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  1. 2-2 Properties from Algebra Notes on worksheet

  2. Properties from Algebra • See Worksheet! Addition Property Subtraction Property Multiplication Property Division Property You can +/-/x/÷ the same number on both sides of an equation

  3. Properties from Algebra • Substitution: think “replace” • Ex: a+b=c, if c = 8 then a + b = 8 • Questions on Substitution??? • We use this ALOT in Proofs! • Reflexive: a # equals itself (same on both side) • Symmetric: switch the side of the equal sign it is on • Transitive (3 parts) • Ex: 6 + 4 = 10 5 • 2 = 10 6 + 4 = 5 • 2

  4. Properties from Algebra • Properties of Congruence: Properties of Equality where the equal sign is replaced with a congruency sign. • Distributive Property • If a(b + c), then ab + ac • What do you notice about all the properties? • They are If-Then statements!

  5. Example • Justify the statement: If WX = YZ, then WY = XZ addition: we added the segment XY to both sides of the original equation W Z X Y

  6. Example • Justify the statement: If WY = XZ, then WX = YZ subtraction: we subtracted the segment XY from both sides of the original equation W Z X Y

  7. TOO—on Whiteboards!!!! • If 4x = -24, then x = -6 • DIVISION! • If a = b and b = c then a = c. • Transitive! • Angle A = Angle A • Reflexive!

  8. Homework • Worksheet 2-1 and 2-2 • Skip #14 the Proof, We will do it together tomorrow

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