# Congruency in bow-tie triangles

We've just started congruency in my class, and we've stumbled across a question which goes like this:

Prove that ∆AOB $\equiv$ ∆COD

I drew up a diagram which portrays exactly the same information yet makes it impossible to prove that $\angle$AOD = 180°.

• $\angle AOD$ must be 180 degrees, otherwise you cannot apply the side-angle-side rule: AOD and BOC are two crossing lines so to speak. – Nicky Hekster May 6 '14 at 8:02