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Algebraic Properties for Equations

Explore addition, subtraction, multiplication, division properties in algebra with substitution methods for equations. Learn about reflexive, symmetric, transitive properties and properties of congruence. Practice with distributive property and if-then statements. Homework includes worksheet 2-1 and 2-2 (skip #14).

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Algebraic Properties for Equations

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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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