ABCD is a rectangle in which diagonal AC bisects `/_A`as well as `/_C`. Show that:(i) ABCD is a square (ii) diagonal BD bisects `/_B`as well as `/_Ddot`.

Explanation

(i)`ABCD` is a rectangle , in which diagonal AC bisect `/_A \ as well as \ /_C`
Therefore,`/_DAC=/_CAB`(1)
`/_DCA=/_BCA`(2)

A square is a rectangle when all sides are equal.
Now,
`AD∥BC \and\AC` is transversal.
`/_DAC=/_BCA` (Alternate angles)
From (1),`/_CAB=/_BCA`(3)
In `/_\ABC,/_CAB=/_BCA`
`BC=AB` (4)(sides opposite to equal angles)
But `BC=AD and AB=DC`(5) (Opposite sides of rectangle)
Therefore from (4)& (5),`AB=BC=CD=AD`
Hence, `ABCD` is a square.
`(ii) ABCD` is a square and we know that diagonals of a square bisect its
angles.
Hence, BD bisects `/_B \as well as\ /_D`.