How to Prove a Quadrilateral Is a Parallelogram


Quadrilaterals and parallelograms are geometrical figures that you might encounter in a middle school, high school or college math or geometry class. While the term "quadrilateral" applies to any four-sided two-dimensional figure, a parallelogram is a type of quadrilateral that meets certain qualifications. You can prove that a quadrilateral is a parallelogram by identifying and checking for the five specific criteria that apply to parallelograms.

  • Look to see if opposite sides are parallel. Parallel lines run in the same directions and never meet. If both pairs of opposite sides are parallel, the quadrilateral is a parallelogram.

  • Look at the length of the quadrilateral's sides. If each pair of the quadrilateral's opposite sides is the same length, the figure is a parallelogram.

  • Look at the combination of length and the quality of being parallel once more. If at least one pair of opposite sides is both congruent (line segments of the same length) and parallel, you have a parallelogram.

  • Draw straight diagonal lines from opposite angles within the quadrilateral. If these lines bisect each other (cut each other exactly in half at the point of intersection), the figure is a parallelogram.

  • Look at the corners of the quadrilateral. If the angles of both sets of opposite corners are the same measurements, the quadrilateral is also a parallelogram.

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