Question

prove that diogonals of a rhombus bisect at 90 degree

Answer 1

Occurred a rhombus ABCD
To prove : Angle AOD = 90°
We know that AB = BC = CD = DA
Now, in triangle AOD and COD ,
OA = OC ( diagonal of a rhombus bisect each other )
OD = OD ( common )
AD = CD ( we know )
Therefore, triangle AOD = triangle COD ( SSS congruence rule )
This gives, angle AOD = angle COD ( CPCT )
But, angle AOD + angle COD = 180° ( linear pair )
So, 2angle AOD = 180°
or, angle AOD = 90°
SO, the diagonals of a rhombus are perpendicular to each other.


....hope this helps you.