I am looking for an elegant elementary, preferrably geometric proof of the following theorem:
It states that $a + b = x + y$.
My proof is as follows:
- $ABD = 180^\circ - x$ (adjacent angles);
- $ACD = 180^\circ - y$ (adjacent angles);
- $\angle BAC + \angle ACD + \angle BDC + \angle ABD = 360^\circ$ (sum of angles of a convex quadrilateral);
- $a+b+180^\circ - x + 180^\circ - y = 360^\circ$
- $a+b-x-y = 0$
- $a+b = x+y$, which was to be proven.
I would also like to know the name of this theorem too, if any.