Show reasons in geometry?

Question

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

 

_____________________________

A     B                                 C      D

 

I've figured out a few of the reasons, I'm having trouble figuring out the rest, though.

 

Statements:                           Reasons:

AC=BD                                  transitive property of equality

AC=AB+BC                            definition of between

AB+BC=BD                            ??

BD=BC+CD                            ??

AB+BC=BC+CD                     addition property of equality

AB=CD                                  ??

CD=AB                                  ??

CD≅AB

Answer 1

AC=BD     Given

AC=AB+BC    Segment Addition Postulate

BD=BC+CD   Segment Addition Postulate

BD=AB+BC   Substitution (substituted BD for AC because AC=BD was Given)

AB+BC=BC+CD  Transitive Property of Equality

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

AB+0=0+CD    Addition Property of Opposites

AB=CD  Addition Property of Zero or Additive Identity Property

AB≅CD  Congruence Property (If 2 line segments have the same length then they are congruent)