2025 MGS(S) PRELIMS P1 Q14

The diagram shows a trapezium \(ABCD\), where \(AB\) is parallel to \(DC\). \(AC\) and \(BD\) are its diagonals. \(E\) is a point on \(BD\) such that \(5DE=4EB\).

1. Show that triangle \(ABE\) and triangle \(CDE\) are similar.[2]
2. Calculate
   1. \(\dfrac{\text{area of triangle}\hspace{0.5em}ABE}{\text{area of triangle}\hspace{0.5em}CDE}\),[1]
   2. \(\dfrac{\text{area of triangle}\hspace{0.5em}ABE}{\text{area of triangle}\hspace{0.5em}ABC}\).[1]