The problem reads:

If $\displaystyle \bigtriangleup KLT$ $\displaystyle \cong$ $\displaystyle \bigtriangleup KLM$ and M and T are on the same side of line KL, must M = T?

If so, why? If not, sketch a figure in which M $\displaystyle \neq$ T.

The hint our teacher gave was that $\displaystyle \angle$K $\displaystyle \cong$ $\displaystyle \angle$K. So I attempted to draw a figure to help me figure this out, but I got stuck with the criterion that M and T are on the same side of line KL.

Here's my figure:

Should I have drawn two separate triangles?

I just am quite confused with what the instructions are specifically asking.

Our teacher said this problem should not take much time since it is not a proof, and if we've been working on it for more than 5 minutes then we're overthinking it.

I've been stuck on this problem since yesterday afternoon

Any help is greatly appreciated! Thanks!