Question

The diagonals of a kite bisect each other.

• A. True
• B. False

Answer 1

The correct option is B

False

In $\Delta ABD$ and $\Delta CBD$
AB = CB --------- (Properties of kites)
AD = CD --------- (Properties of kites)
BD = BD (Common side)
So, by SSS congruence rule:
$\Delta ABD$ $\cong$ $\Delta CBD$
$\angle ABD$ = $\angle CBD$ (By C.P.C.T) ------(i)
In $\Delta AOB$ and $\Delta COB$
AB = CB (Properties of kite)
OB = OB (Common side)
$\angle ABD$ = $\angle CBD$ ------from (i)
So, $\Delta AOB$ $\cong$ $\Delta COB$ by SAS congruence
$\therefore$ AO = CO (By C.P.C.T)
So, diagonal BD bisects AC.
But $\Delta ODC$ is not congruent to $\Delta OBC$.
OD $\ne$ OB and diagonal AC doesn't bisect BD.
Hence, diagonals of a kite do not bisect each other.