Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that

Question

Philoid · Accepted Answer

In ΔDOC and ΔBOA,

∠CDO = ∠ABO (Alternate interior angles as AB || CD)

∠DCO = ∠BAO (Alternate interior angles as AB || CD)

∠DOC = ∠BOA (Vertically opposite angles)

Therefore,

(Corresponding sides are proportional)

,