MathNet 2015-part-01 — 191 problems (EN–VI) Question 141

In the figure below, $ABCD$ is a square and the points $K$, $L$ and $M$ lie on the sides $AB$, $BC$ and $CD$ so that $\triangle KLM$ is an isosceles triangle, right-angled at $L$. Prove that $AL$ and $DK$ are perpendicular.