What is the geometric derivation of 2D Fraunhofer aperture diffraction?

In this derivation, I can understand the formulas stated for 1D diffraction for both x andy (with the phase difference $\delta= ksin\theta y$ ) in the far-field limit, but how can we just sum the phases from both the x and y components in such a simple manner? I would expect a formula like pythagoras would be needed instead of just $\delta = k(sin(\phi) x + sin(\theta)y)$ .