Question

Prove that each diagonal of a rhombus bisects the angle through which it passes

Answer 1

Let, ABCD be a rombus and the vertex where their diagonal intersect be 'O'

Then in triangle AOD and DOC
As;
AD = DC
OD = OD
angle AOC = AOD
So triangle AOD = DOC

As angle AOD = DOC
and AOD + DOC = 180
2 AOD = 180
AOD = 90

So as opposite angles are equal when two lines intersect so all four angles are 90°