Q4 of 49 Page 151

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.


In ΔAOB and ΔCOD


AO = CO … given


∠AOB = ∠COD … vertically opposite angles


BO = OD … given


Therefore, by SAS test for congruency


ΔAOB ≅ ΔCOD


⇒ AB = CD … corresponding sides of congruent triangles


Hence proved AB = CD


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