2.4 Reasoning with Properties from Algebra

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Presentation transcript:

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 GIVEN Subtraction Property of Equality Addition Property of Equality Division Property of Equality

Solve Solve 5x – 18 = 3x + 2 and explain each step in writing. 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 Given Distr. Property Combine Like Terms Add POE Div POE

Properties of Equality Segment Length Angle Measure Reflexive AB = AB m<A = m<A Symmetric If AB = CD, then CD = AB. If m<A = m<B, then m<B=m<A. Transitive If AB = CD and CD = EF, then AB=EF. If m<A = m<B and m<B=m<C, then m<A=m<C.

Given AB=CD, show that AC=BD Statements Reasons AB=CD Given AB + BC = CD + BC Addition Prop of Equality Segment Addition Postulate AB + BC = AC Segment Addition Postulate BC + CD = BD AC = BD Substitution Prop of Equality

Given: 4 2 3 1 Find:

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.