Question 18
Let $AB\Gamma\Delta$ ($A\Delta\parallel B\Gamma$) be a trapezium with $\hat{A} = \hat{B} = 90^\circ$ and $A\Delta \lt B\Gamma$. Denote by $E$ the point of intersection of the two non parallel sides $AB$ and $\Gamma\Delta$, $Z$ the symmetric point of $A$ with respect to the line $B\Gamma$ and $M$ the midpoint of $EZ$. It is given that the line $\Gamma M$ is perpendicular to the line $\Delta Z$. Prove that the line $Z\Gamma$ is perpendicular to the line $\Gamma E$.