Understanding Equivalency in Simple Geometry: A, B, C, and D Explained

[Bashyboy]

The question is "Is it ever correct to write $\stackrel{\Large\leftrightarrow}{AB} = \stackrel{\Large\leftrightarrow}{CD}$. If so, what does that imply about A, B, C, and D.

I feel like this statement of equivalency would only be true in the circumstance that A and C were two different names for the same point, and this being similar for B and D. Is this accurate?

 

[HallsofIvy]

The question is "Is it ever correct to write $\stackrel{\Large\leftrightarrow}{AB} = \stackrel{\Large\leftrightarrow}{CD}$. If so, what does that imply about A, B, C, and D.

I feel like this statement of equivalency would only be true in the circumstance that A and C were two different names for the same point, and this being similar for B and D. Is this accurate?

The statement "A= B" means "A and B represent the same object".

You statement says that ${\Large\leftrightarrow}{AB}$ and $\stackrel{\Large\leftrightarrow}{CD}$ represent the same line. That will be true if and only if C and D lie on the same line as A and B.