2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

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Presentation transcript:

2.5 Reasoning and Algebra

Addition Property If A = B then A + C = B + C

Subtraction Property If A = B then A – C = B - C

Multiplication Property If A = B then AC = BC

Division Property If A = B and C is not 0 then A/C = B/C Why cant C = 0?

Substitution Property If A = B then A can be substituted for B in any equation

Distributive property A(B + C) = AB + AC

Reflexive Property For real numbers: A= A For Segments AB = AB For angles m<A = m<A

Symmetric Property For real numbers: if A = B then B = A For segments: if AB = CD then CD = AB For angles: If m<A = m<B then m<B = m<A

Transitive Property For real numbers: If A = B and B = C then A = C For Segments: if AB = BC and BC = CD then AB = CD For angles: if m<A = m<B and m<C = m<D then m<A = m<C

Proofs This is an explanation of what you are doing to solve a problem or prove a theory You use the rules you know to do this

2 Column Proof

Proofs

2x + 15 = 3x = x = x X = 5 Given Subtraction Symmetric

5X – 9 = 3X + 1 2X – 9 = 1 2X = 10 X = 5 Given Subtraction Addition Division

2(X – 5) = 3X + ½ 2X – 10 = 3X + ½ -10 = X + ½ -20 = 2X = 2X = X X = Given Distributive Subtraction Multiplication Subtraction Division Symmetric