Given ABCD is a trapezium in which BC || AD and AD = 4 cm.

Also, the diagonals AC and BD intersect at O such that

In ΔAOD and ΔCOB,

∠OAD = ∠OCB [alternate angles]

∠ODA = ∠OBC [alternate angles]

∠AOD = ∠BOC [vertically opposite angles]

We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

∴ ΔAOD ~ ΔCOB

We know that two triangles are similar if their corresponding sides are proportional.

∴ BC = 8 cm