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2.4 Reasoning with Properties from Algebra Algebraic Properties of Equality • 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≠0, then a/c = b/c. Writing reasons 5 x 18 3 x 2 GIVEN 2 x 18 2 Subtraction Property of Equality 2 x 20 Addition Property of Equality x 10 Division Property of Equality Solve • Solve 5x – 18 = 3x + 2 and explain each step in writing. 5x – 18 = 3x + 2 2x – 18 = 2 2x = 20 x = 10 Subtraction p. of e. Addition p. of e. Division p. of e. More properties of equality • Reflexive property: For any real number a, a=a. • Symmetric property: If a=b, then b=a. • Transitive property: If a=b and b=c, then a=c. • Substitution property: If a=b, then a can be substituted for b in any equation or expression. Writing Reasons 55 z 3(9 z 12) 64 Given 55 z 27 z 36 64 Distr. Property 28 z 36 64 Combine Like Terms 28 z 28 Add POE z 1 Div POE Properties of Equality Reflexive Segment Length AB = AB Symmetric If AB = CD, then CD = AB. Transitive If AB = CD and CD = EF, then AB=EF. Angle Measure m<A = m<A If m<A = m<B, then m<B=m<A. If m<A = m<B and m<B=m<C, then m<A=m<C. A B C D Given AB=CD, show that AC=BD Statements Reasons AB=CD Given AB + BC = CD + BC Addition Prop of Equality AB + BC = AC Segment Addition Postulate BC + CD = BD AC = BD Segment Addition Postulate Substitution Prop of Equality 2 4 3 Given: m 1 m 2 m 3 180 m 1 m 2 93 m 3 m 4 180 1 Find: m 4 Review • Let p be “a shape is a triangle” and let q be “it has an acute angle”. – Write the contrapositive of p q. – Write the inverse of p q.