Unizor - Geometry2D - Parallelogram
Channel: Zor Shekhtman on UNIZOR Education
Date: 2011-10-20

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A quadrangle (polygon with 4 vertices) ABCD with pairs of opposite sides parallel to each other (i.e. AB || CD and BC || AD) is called parallelogram.
Here are the most important properties of parallelograms.
1.Two angles of a parallelogram formed by any one side with both its neighboring sides are supplemental to each other.
2.Parallel sides of a parallelogram are congruent.
3.If two pairs of opposite sides of a convex quadrangle are congruent then this is a parallelogram.
4.Opposite angles of a parallelogram are congruent.
5.If two opposite sides BC and AD of quadrangle ABCD are parallel and congruent to each other then this quadrangle is a parallelogram.
6.Distance between parallel lines measured along any mutual perpendicular is constant and does not depend on where this mutual perpendicular is drawn.
7.A point of intersection of diagonals in a parallelogram divides each diagonal into two congruent parts.
8.If a point of intersection of two diagonals in a quadrangle divides each diagonal into two congruent parts then a quadrangle is a parallelogram.
9.Sequentially connected midpoints of all sides of any quadrangle form a parallelogram.