Angle bisector always passes through vertex of original angle?
If the angle bisector of an angle of a parallelogram passes through the vertex opposite to it, then the parallelogram will be a rhombus.
A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α where 0<α<90with the positive direction of x - axis. The equation of its diagonal not passing through the origin is