(related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
If two adjacent sides of a parallelogram are equal in length, then all its sides are equal in length and it is a rhombus.
Equivalent definitions are:
The diagonals of a parallelogram are perpendicular to each other.
A diagonal of a parallelogram bisects the angles whose vertices it joins.
Proofs: 1
Corollaries: 1