Question

Suppose ABCD is a parallelogram in which AB =CD and AC perpendicular to BD, then prove that the figure so made is a square by showing congruency ?

Answer 1

let diagonals met at o.
in ABO AND DOC
DC=AB
AOB=DOC
ABO=ODC
THRFORE ., OD,=OB... CPCT
IN AOB AND DOA
AO=AO
AOD=AOB
DO=OB (PROVED ABOVE)
THEREFORE., AD=AB SIMILARLY AB=BC
THERFORE AD=AB=DC=BC
HENCE PROVED