a + c = b + c a - c = b - c ac = bc a c b = a can be

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Presentation transcript:

a + c = b + c a - c = b - c ac = bc a c b = a can be substituted for b in any equation or expression

2x + 3 = 9 - x +x +x x Addition Property of Equality ___________ 3x + 3 = 9 -3 -3 _________ 3x = 6 Subtraction Property of Equality 3 3x = 6 3 x = 2 2 Division Property of Equality

ab + ac -24x - 8 Distributive Property of Equality -24x 72 8 Addition x -3 Division -24

x - 5 = 7 + 2x Given -5 = 7 + x Subtraction Property of Equality -12 = x Subtraction Property of Equality 4(5 - x) = -2x Given 20 - 4x = -2x Distributive Property of Equality 20 = 2x Addition Property of Equality 10 = x Division Property of Equality

3.5s - 17.5 Distributive Property 17.5 3.5s 17.5 Addition 17.5 3.5 Division d + = s or

a = a AB = AB m∠A = m∠A KT = KT because it's the same length in both triangles b = a CD = AB m∠B = m∠A The Symmetric Property is pretty straightforward but it isn't used too often. a = c AB = EF m∠A = m∠C The Transitive Property is similar to the Law of Syllogism because the output of one statement is the input of another. These properties are regularly used as reasons in Two-Column proofs.

This is really an example of a Two-Column proof This is really an example of a Two-Column proof. The column on the left are Statements and the column on the right are Reasons. EF (it's given info b/c of the congruence symbols) DE Segment Addition Postulate DE EF Substitution AC Transitive AC Addition CF AD

d = 5(s + 3) Given d 5 = s + 3 Division Property - 3 = s Subtraction Property d = 5s + 15 Distributive Property d - 15 = 5s Subtraction Property - 15 = s Simplify OR Symmetric Property of Equality Transitive Property of Equality Reflexive Property of Equality