A blog for enthusiastic math-lovers!

Clever Geometry Problem

Another interesting problem!

Suppose you have a quadrilateral ABCD where AB is parallel to CD and such that the length of DA = AB = BC and BD = DC.
What are the angles of this quadrilateral?

Hint: Obviously, a trigonometry solution is possible with some work. But there’s another way, without writing down a single number! Keep in mind your shapes and rules about certain, specific edges being equal to one another as in this problem.

1. A pretty interesting problem. Thanks for this. I tried doing a quick sketch of the solution. Hopefully, there’s no flaw. The shape is a parallelogram with angles, $\frac{\pi}{3}$ and $\latex {2 \pi}{3}$
• Sorry, I meant, and $\latex \frac {2{\pi}}{3}$