HMMT 2019 T1

Let $A B C D$ be a parallelogram. Points $X$ and $Y$ lie on segments $A B$ and $A D$ respectively, and $A C$ intersects $X Y$ at point $Z$. Prove that

$$\frac{A B}{A X}+\frac{A D}{A Y}=\frac{A C}{A Z}$$