What are the reasons for these statements...

For example:Statement(AC=BD)Reason(Given)

For example:Statement(AC=AB+BC)Reason(Segment addition postulate)

Statement(AB+BC=BD)Reason?

Statement(BD=BC+CD)Reason?

Statement(AB+BC=BC+CD)Reason?

Statement(AB=CD)Reason?

Statement(CD=AB)Reason?

Statement(Line segment CDcong Line segment AB)Reason?

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For example:Statement(AC=BD)Reason(Given)

For example:Statement(AC=AB+BC)Reason(Segment addition postulate)

Statement(AB+BC=BD)Reason?

AB+BC=AC (addition postulate)

AB+BC=BD ( AC=BD ) (given)

Statement(BD=BC+CD)Reason?

Segment addition postulate.

Statement(AB+BC=BC+CD)Reason?

AB+BC=AC (Segment addition postulate)

BC+CD=BD (Segment addition postulate)

AC=BD (given)

Statement(AB=CD)Reason?

AC= BD (given)

AC-BD=0

AB+BC-(BC+CD)=0

AB-CD=0

AB=CD

Statement(CD=AB)Reason?

AC= BD (given)

BD-AC=0

(BC+CD)-(AB+BC)=0

CD-AB=0

CD=AB

Statement(Line segment CDcong Line segment AB)Reason?

Lenth of line AB= length of line CD ( AB=CD given)

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