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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