12. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

Question

12.   Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

anonymous · Answer

Given:

anonymous · Answer

and...

anonymous · Answer

attachment

anonymous · Answer

it is a parallelogram but I need to think of a reason besides "cuz I said so" :/

anonymous · Answer

I can't think of a geometry def'n as to why. 

Where both lines intersect you could say the equal vertical angles proves that the opposite sides are equal. But how does that prove parallelism?... hmm

You could solve for the other angles but that is a lot of work

anonymous · Answer

Ohh. I'd rather just skip this question. But, thanks anyways.

anonymous · Answer

Opposite angles are Congruent so it must be a Parallelogram

anonymous · Answer

Because the diagonals have equal length on either side of the point of intersection, the figure is a parallelogram. This is proved by Theorem 6-3 (The diagonals of a parallelogram bisect each other). I just wanted to post this so you know, even if you're done with the question. :)