prove that two triangles are congruent if they have 2 equal adjacent angles and the side inbetween them is also the same.

Answer 1

A side and the two angles at either end completely define the point where the two other sides intersect. Thus all sides and angles are reproduced for both triangles and the triangles are congruent.

That is not the way they want you to wrte geometric proofs, but I hope you can fill in the gaps.

Answer 2

You might try this geometry link:

http://www.themathpage.com/abooki/propI-26.htm

Answer 3

ASA