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2-4 Reasoning in Algebra (7 cards) Addition/Subtraction Property Add or subtract the same number from both sides of an equation 4 + x = 12 -4 -4 X=8 (Subtraction Property) Multiplication/Division Property Multiply or divide the same number on each side of an equation 8x = 56 8 8 X=7 (Division Property) Reflexive Property A number, segment or angle is equal or congruent to itself 5=5 c=c AB AB A A Symmetric Property Two equal numbers, segments or angles are equal or congruent to its converse If a = b, then b = a If AB CD then CD AB If A B then B A Transitive Property The law of syllogism applied to numbers, segments and angles If a = b and b = c, then a = c If AB CD and CD EF, then AB EF If A B and B C, then A C Substitution Property Equivalent numbers, segments and angles can replace each other If a = b then a can repalce b in any expression or equation If AB CD then AB can replace CD in any expression or equation If A B then A can replace B in any expresion or equation Distributive Property a(b + c) = ab + ac Ex 1 Justify each step to solve for x given mAOC = 139 B x A O (2x + 10) C Ex 1 Justify each step to solve for x mAOC = 139 Given B x A O (2x + 10) C Ex 1 Justify each step to solve for x mAOC = 139 Given mAOB + mBOC = mAOC Angle Addition Postulate B x A O (2x + 10) C Ex 1 Justify each step to solve for x mAOC = 139 Given mAOB + mBOC = mAOC Angle Addition Postulate x + 2x + 10 = 139 Substitution x A O B (2x + 10) C Ex 1 Justify each step to solve for x mAOC = 139 Given mAOB + mBOC = mAOC Angle Addition Postulate x + 2x + 10 = 139 3x + 10 = 139 Substitution Simplify Ex 1 Justify each step to solve for x mAOC = 139 Given mAOB + mBOC = mAOC Angle Addition Postulate x + 2x + 10 = 139 3x + 10 = 139 3x -10 -10 = 129 Substitution Simplify Subtraction Property Ex 1 Justify each step to solve for x mAOC = 139 Given mAOB + mBOC = mAOC Angle Addition Postulate x + 2x + 10 = 139 3x + 10 = 139 3x 3 -10 -10 = 129 Substitution Simplify Subtraction Property 3 x = 43 Division Property Ex 2 Justify each step to solve for x Suppose points A, B and C are collinear with point B between points A and C. Solve for x if AB = 4 + 2x, BC = 15-x and AC = 21 Ex 3 Justify each step to solve for x Given ray LM bisects angle KLN. The measure of angle KLM is 2x+40 and the measure of angle MLN is 4x. Homework