Quadrilateral congruency theorem Is there a congruence theorem that says that if three sides of two quadrilaterals are equal, then the two quadrilaterals are congruent? I am grading some homework and a student appealed to such a theorem, but I cannot find it anywhere. I'd like to give them credit if it is the case...

I'm sorry, but the student is out of luck. No there isn't such a theorem, and for good reason. Indeed, if all four sides of a quadrilateral are equal in length to the sides of another quadrilateral, _even then_ we cannot conclude the quads are congruent.

A simple counter-example suffices:

> Consider an $(a \times a)$ **square** , vs. a (non-square) _**rhombus**_ whose sides are all of length $a$, but do not meet at right angles, exemplified nicely in the image below:

!enter image description here

Image from Wikipedia rhombus