Question

if the diagonal of a quadrilateral bisect each other then quadrilateral all parellelogram.prove it

Answer 1

in quad. ABCD
AC And BD ARE DIAGONAL INTERSECTING AT POINT O.
DRAW DIAG. BY THIS CONDITIONS
IN TR. AOB AND TR. COD
         AO=CO                          (AC AND BD BISECT EACH OTHER)
         ANGLE'S(AOB=COD)   (VERT. OPP.ANGLE.) 
         BO=DO
 TR. AOB IS CONGRUENT TO TR.COD (BY SAS )
AB = CD  (CPCT)
SIMILARLY, AD = BC (BY TAKING TR'S AOD AND BOC)

THEREFORE , OPP. SIDES OF QUAD. ARE EQUAL AND ITS DIAGONAL BISECT EACH OTHER , 
HENCE IT IS A PARALLELOGRAM

Answer 2

parallelogram, square, rectangle and rhombus

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