Let P be the point where BY and CZ meet. Assume that BY=CZ and PY=PZ. Show that AB=AC.

Question

I've been able to prove that ΔBPC is isosceles using given information that CZ=BY, but I am at a loss with how to prove that ΔBPZ≅ΔCPY. If I could prove this I could show that AB=AC since the equal base angles would make it an isosceles triangle.

Answer 1

$BP=CP$, $PZ=PY$ and $\angle BPZ = \angle CPY$: SAS criterion.