Question

ABCD is a quadrilateral in which diagonals AC and BD bisect each other at O prove that AB and DC are equal and parallel.

Answer 1

Given ABCD is a quadrilateral where
OA=OC and OB = OD
To prove: AB=CD and AB||CD
Proof: In ΔAOB and ΔCOD, we have
AO= CO
BO = DO
<AOB = <COD
So, by SAS congruency criterion we have.
ΔAOB is congruent to ΔCOD
Hence AB= CD (by cpct)
Similarly, ΔAOD is congruent to ΔBOC
So, AD=BC
So, ABCD is a parallelogram
So, AB || CD...... Proved