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**Geometry -- Help with theorem proof please**

## Homework Statement

Let ##A,B,C,D## be points. If ##\vec{AB} = \vec{CD}## then ##A=C##.

## Homework Equations

None

## The Attempt at a Solution

This question was a theorem in my book that wasn't proved. I am wondering how to prove it?

It is saying that the vertex ##A## must equal ##C## if the ray ##\vec{AB} = \vec{CD}##.

The definition I have for ray is:

##\vec{AB} = \vec{AB} \cup \{ C \in P \ | \ A-B-C\}.## Where ##A-B-C## means ##B## is between ##A## and ##C##. And ##P## is the set of points.

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