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How to Prove a Parallelogram

In mathematics, the basic shape of the parallelogram falls into the category of quadrilaterals, or shapes with four sides and, thus, four angles. Mathematicians define the parallelogram through a list of physical characteristics that distinguish it from other quadrilaterals such as kites and isosceles trapezoids. Squares, rectangles and rhombuses are types of parallelograms. To prove that a quadrilateral is a parallelogram, you must ensure the shape satisfies all the rules and theorems for a parallelogram.

Ruler
Protractor

Instructions

- 1
  Measure the opposite angles to determine they are equal, or congruent.
- 2
  Add the two adjacent angles to confirm they total 180 degrees, making them supplementary angles. The angles may be right angles, making the parallelogram a square or rectangle.
- 3
  Measure both sets of opposite sides to determine they are congruent -- that is, the sum of two adjacent angles equals the sum of the opposite two adjacent angles. All four angles may be congruent, but only the opposite pairs must be congruent to be a paralellogram.
- 4
  Determine that both sets of opposite sides are parallel.
- 5
  Draw a line from one angle to the opposite angle and scrutinize the resulting triangles to determine they are congruent triangles.
- 6
  Draw the other diagonal line from one angle to the opposite angle, and measure these diagonal lines to ensure they bisect each other, or split each other exactly in half.

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