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Properties of a Parallelogram

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Properties of a Parallelogram - Lesson Summary

A parallelogram is a quadrilateral in which
        •  opposite sides are parallel and equal,
        •  opposite angles are equal,
        •  the diagonals bisect each other,
        •  each diagonal divides it into two congruent triangles,
        •  adjacent angles are supplementary.

A square is a parallelogram in which
        •  all the sides are equal,
        •  each angle measures 90°,
        •  diagonals are equal and bisect at right angles.

A rectangle is a parallelogram in which
        •  diagonals are equal and bisect each other,
        •  each angle measures 90°.

A rhombus is a parallelogram in which
        •  all the four sides are equal,
        •  diagonals bisect each other at right angles.



A diagonal of a parallelogram divides it into two congruent triangles.
ABCD is a parallelogram and AC is a diagonal. ΔABC ≅ ΔCDA.

 

If each pair of opposite sides is equal in a quadrilateral, then it is a parallelogram.
ABCD is a quadrilateral. If AB = CD and BC = AD, then ABCD is a parallelogram.
               


If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
ABCD is a quadrilateral and the diagonals AC and BD intersect at E.
If BE = DE and AE = CE then, ABCD is a parallelogram.
                  

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