2 Properties from Algebra See Worksheet!Addition PropertySubtraction PropertyMultiplication PropertyDivision PropertyYou 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 = 8Questions 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 onTransitive (3 parts)Ex: = • 2 = 106 + 4 = 5 • 2
4 Properties from Algebra Properties of Congruence: Properties of Equality where the equal sign is replaced with a congruency sign.Distributive PropertyIf a(b + c), then ab + acWhat 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 segmentXY to both sides of theoriginal equationWXYZ
6 Example Justify the statement: If WY = XZ, then WX = YZ subtraction: we subtracted thesegment XY from bothsides of the originalequationWXYZ
7 TOO—on Whiteboards!!!! If 4x = -24, then x = -6 DIVISION! If a = b and b = c then a = c.Transitive!Angle A = Angle AReflexive!
8 Homework Worksheet 2-1 and 2-2 Skip #14 the Proof, We will do it together tomorrow