2.4 Reasoning with Properties from Algebra

1. 2.4 Reasoning with Properties from Algebra

2. 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.

3. Writing reasons GIVEN Subtraction Property of Equality Addition Property of Equality Division Property of Equality

4. 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.

5. 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.

6. Writing Reasons Given Distr. Property Combine Like Terms Add POE Div POE

7. Properties of Equality

8. A B C D 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

9. Given: 4 2 3 1 Find:

10. 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.