The triangle XYZ and the triangles XWZ and YWZ are right triangles.

Since,

\(\displaystyle\angle{Z}{W}{X}=\angle{Y}{Z}{X}=\angle{Y}{Z}{W}={90}^{{\circ}}\)

Also, midpoint of line XY divide the base proportionally.

Therefore, the sides are also proportional.

Therefore, by the rules of similarity, the triangles are proportional.

Since,

\(\displaystyle\angle{Z}{W}{X}=\angle{Y}{Z}{X}=\angle{Y}{Z}{W}={90}^{{\circ}}\)

Also, midpoint of line XY divide the base proportionally.

Therefore, the sides are also proportional.

Therefore, by the rules of similarity, the triangles are proportional.