# Is a parallelogram a quadrilateral

## How to Prove that a Quadrilateral Is a Parallelogram

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In Euclidean geometry , a parallelogram is a simple non- self-intersecting quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. A simple non-self-intersecting quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3].

I'm thinking of a quadrilateral with one pair of opposite sides parallel and congruent. Name that quadrilateral. I'm thinking of a quadrilateral with both pairs of opposite sides congruent.
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One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel. If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi. If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid.

Quadrilateral just means "four sides" quad means four, lateral means side. A Quadrilateral has four-sides , it is 2-dimensional a flat shape , closed the lines join up , and has straight sides. Also see this on Interactive Quadrilaterals. Try drawing a quadrilateral, and measure the angles. Some types are also included in the definition of other types!

There are five ways in which you can prove that a quadrilateral is a parallelogram. The first four are the converses of parallelogram properties including the definition of a parallelogram. Tip: To get a feel for why this proof method works, take two toothpicks and two pens or pencils of the same length and put them all together tip-to-tip; create a closed figure, with the toothpicks opposite each other. The only shape you can make is a parallelogram. Tip: Take, say, a pencil and a toothpick or two pens or pencils of different lengths and make them cross each other at their midpoints.

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## Properties of parallelograms

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