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

Diagram 1

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°.

Diagram 2

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  • $\begingroup$ $\angle AOD$ must be 180 degrees, otherwise you cannot apply the side-angle-side rule: AOD and BOC are two crossing lines so to speak. $\endgroup$ – Nicky Hekster May 6 '14 at 8:02
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I would assume that they are straight lines, because, as you said, it is false if you assume otherwise.

However, usually some text describing the construction of the figure is nearby, and it would tell you something like "Let O be the intersection of lines AD and BC".

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