Question

Approach

Step-by-step working

1. 1

   Draw correct figure of parallelogram $ABCD$ with point $E$ on extended $AD$ and $BE$ intersecting $CD$ at $F$.

   0.5 marks
2. 2

   (i) In $△DFE$ and $△CFB$: $\angle 5=\angle 3$ (alternate interior angles), $\angle 1=\angle 2$ (alternate interior angles). By AA similarity, $△DFE\sim △CFB$.

   1.5 marks
3. 3

   (ii) In $△AEB$ and $△CBF$: $\angle 1=\angle 2$ (alternate interior angles), $\angle 4=\angle 3$ (opposite angles of parallelogram). By AA similarity, $△AEB\sim △CBF$.

   1 mark

Concepts used