2 4 Reasoning with Properties from Algebra Algebraic
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 5 x – 18 = 3 x + 2 and explain each step in writing. 5 x – 18 = 3 x + 2 2 x – 18 = 2 2 x = 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 Given Distr. Property Combine Like Terms Add POE Div POE
Properties of Equality Reflexive Segment Length AB = AB Angle Measure m<A = m<A Symmetric If AB = CD, If m<A = m<B, then CD = AB. then m<B=m<A. Transitive If AB = CD If m<A = m<B and CD = EF, and m<B=m<C, then AB=EF. 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: 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.
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