Question

Let AB and CD be two line segments such that AD and BC intersect at O. Suppose AO = OC and BO = OD. Prove that AB = CD.

Answer 1

Given: AO = OC and BO = OD

To Prove: AB = CD

Proof:

In ΔAOB and ΔDOC:

AO = OC (Given)

∠AOB = ∠COD (Vertically opposite angles)

BO = OD (Given)

⇒ΔAOB ≅ ΔDOC (SAS congruency)

⇒ AB = CD (Corresponding parts of congruent triangles)