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.
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
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.

8. 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.