showing reasons

Question

in the diagram below AC = BD.  Fill in the reasons to show CD = AB.

 

Given AC = BD

Prove CD = AB           __________________________________

                                A         B                                     C         D

 

 

 

What is the reasons for:

 

AB = CD    is it transitive?

CD = AB    is it symmetric?

AC = AB + BC   is it segment addition prostulate

AB + BC = BC + CD  is it addition property of equality

 

thanks

Answer 1

AC=BD      Given

AC=AB+BC      Segment Addition Postulate

BD=BC+CD     Segment Addition Postulate

AB+BC=BC+CD    Substitution (the left side equals AC and the right side equals BD and AC=BD)

BC=BC    Reflexive Property

AB+BC+(-BC)=BC+(-BC)+CD   Addition Property of Equality

AB+0=0+CD     Additive Inverse Property

AB=CD  Addition Property of Zero