Euclid's Elements
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Definitions, Axioms, and Common Notions
Chapter 1: Neutral Theorems
Chapter 2: Equivalent Forms of the Parallel Axiom
Chapter 3: Saccheri and Lambert Quadrilaterals
Chapter 4: Similarity
Chapter 5: Euclidean Theorems
chapter 6: Analytic Geometry
Visitor Edits or Additions
Theorem 5.1
:
If a quadrilateral has both pairs of opposite sides congruent then it is a parallelogram.
Theorem 5.2
:
If a quadrilateral has one pair of opposite sides that are both congruent and parallel then it is a parallelogram.
Theorem 5.3
:
If a quadrilateral has both pairs of opposite angles congruent then it is a parallelogram.
Theorem 5.4
:
If a quadrilateral has one pair of opposite angles congruent and one pair of opposite sides parallel then it is a parallelogram.
Theorem 5.5
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If a quadrilateral’s diagonals bisect each other then it is a parallelogram.
Theorem 5.6
:
The converse of Theorem 5.1.
Theorem 5.7
:
The converse of Theorem 5.3.
Theorem 5.8
:
The converse of Theorem 5.5.