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Corollary: Rhombus as a Special Case of a Parallelogram

(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.

Table of Contents

Proofs: 1

Mentioned in:

Corollaries: 1

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"