Right triangle altitude theorem/Linear algebra/Fact

Let ${\displaystyle {}A,B,C}$ be a right triangle, with the right angle located at ${\displaystyle {}C}$. Let ${\displaystyle {}h}$ be the altitude through ${\displaystyle {}C}$, and let ${\displaystyle {}D}$ denote the foot of this altitude through the linen given by ${\displaystyle {}A}$ and ${\displaystyle {}B}$.