Rhombus — diagonals perpendicularly bisect each other and bisect the angles

Dependencies: Isoceles: median, altitude, bisector coincide.

Statement

Let $ABCD$ be a rhombus — i.e. a quadrilateral with four equal sides (definition recorded in rhombus-four-sides-equal):

Let the diagonals $AC$ and $BD$ meet at $O$. Then:

1. They are perpendicular: $AC \perp BD$;
2. They bisect each other: $|OA| = |OC|$ and $|OB| = |OD|$;
3. They bisect the angles: $AC$ bisects $\angle BAD$ and $\angle BCD$; $BD$ bisects $\angle ABC$ and $\angle ADC$.