Question

If the diagonal of a quadrilateral bisdc each other . then prove it is a parallelogram.​

Answer 1

Answer:

You can reason out this result as follows :

Note that in the figure , it is given that OA=OC and OB=OD.

$\sf {so} \: \: \: \: \: \: \: \: \: \: \triangle \: AOB \cong \: \triangle \:COD \\ \\ \sf { \therefore} \: \: \: \: \: \: \: \: \: \: \triangle \: ABO \ = \triangle \: CDO \: \\ \\ \sf{from \: this \: \: \: we \: get \: } \: \: \: AB || \: CD \\ \\ \sf{similarly \: \: \: \: BC \: || \: AD} \\ \\ \sf{therefore \: ABCD \: is \: a \: parallelogram.}$