Answer to Question #13885 in Geometry for Orlando Arzola

Question

The Question Marks are what I need to know the answers to. The first statement answer is obviously "Given". I believe the second is "Segment Addition Postulate" for the third one down I have "Transitive Property". Fourth I have "Segment Addition Postulate". Fifth "Transitive Property". Sixth "Addition Property". Seventh and Eighth I put "Symmetric Property" I need to know if this is correct. This is the problem:

In the Diagram below AC=BD. Fill in the reasons to show that line CD=̃AB.
A________B_______________________C____D


Statements/ Reasons (the question marks represent the postulates that I need to identify)

1) AC=BD (?)
2) AC=AB+BC (?)
3) AB+BC=BD (?)
4) BD=BC+CD (?)
5) AB+BC=BC+CD (?)
6) AB=CD (?)
7) CD=AB (?)
8) CD=̃AB (?)

Answer 1

1) AC=BD & (Given)
2) AC=AB+BC (Segment Addition Postulate)
3) AB+BC=BD (Transitive Property)
4) BD=BC+CD (Segment Addition Postulate)
5) AB+BC=BC+CD (Transitive Property)
6) AB=CD (Addition Property)
7) CD=AB (Symmetric Property)
8) CD=̃AB (Symmetric Property)