Reasoning w/ properties Reasoning w/ properties from Algebrafrom Algebra

Properties of Equality with Properties of Equality with SegmentsSegments

• Reflexive property of equality-Reflexive property of equality-

for any AB, AB=AB.

• Symmetric Prop of equality-Symmetric Prop of equality-

if AB=BC, then BC=AB.

• Transitive Prop of Equality-Transitive Prop of Equality-

if AB=BC & BC=CD, then AB=CD.

Properties of Equality with AnglesProperties of Equality with Angles

• Reflexive Prop of Equality-Reflexive Prop of Equality-

for any <A, m<A=m<A.

• Symmetric Prop of Equality-Symmetric Prop of Equality-

if m<A=m<B, then m<B=m<A.

• Transitive Prop of Equality-Transitive Prop of Equality-

if m<A=m<B & m<B=m<C, then m<A=m<C.

Ex: Write an argument for the Ex: Write an argument for the statement. If AB=CD, then AC=BD.statement. If AB=CD, then AC=BD.

1.1. AB=CDAB=CD

2.2. AB+BC=CD+BC*AB+BC=CD+BC*

3.3. AB+BC=ACAB+BC=AC

CD+BC=BDCD+BC=BD

4.4. AC=BDAC=BD

* Just added a BC to * Just added a BC to each side.each side.

1.1. GivenGiven

2.2. Addition prop of =Addition prop of =

3.3. Segment + postSegment + post

4.4. Substitution prop Substitution prop of =of =

A B C D