WAEC 2025 · Paper 1 · Q37✱✱

In the diagram, $AC$ and $BD$ meet at $E$ , $AB \parallel DC$ , $|AB| = 12\text{ cm}$ , $|AE| = 8\text{ cm}$ and $|DC| = 9\text{ cm}$ . Find $|EC|$ .

Worked solution (try it first)

$AB \parallel DC$ , so the alternate angles at $A$ and $C$ are equal, and so are those at $B$ and $D$ .
Triangles $ABE$ and $CDE$ are similar.
Matching sides are in the same ratio: $\dfrac{EC}{AE} = \dfrac{DC}{AB}$ , so $\dfrac{EC}{8} = \dfrac{9}{12}$ .
$EC = 8 \times \frac34 = 6$ cm, option A.