Q:

# What is the diagonal of a quadrilateral?

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A diagonal is a line between two vertices of a polygon that is also not a side of the polygon, and a quadrilateral is a four-sided polygon. Veritces are the points where sides of a polygon meet, and a polygon is an enclosed figure formed by three or more line segments. Using the diagonal formula n(n-3) / 2 where n is the number of sides, each quadrilateral has two diagonals.

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Credit: freakinhippie CC-BY-2.0

There are a variety of diagonals that are found with different quadrilaterals. Mutually bisecting diagonals cut each other in half, as the two pieces of each diagonal are equal. Parallelograms, rhombuses, squares and rectangles contain mutually bisecting diagonals. Perpendicular diagonals produce right angles where they meet. Squares, rhombuses and kites all fit this category.

Perpendicular bisecting diagonals occur when either of the two types of diagonals form four 90-degree angles where they meet and cut each other in half. A rhombus and square both fulfill this requirement. A trapezoid is the only quadrilateral that has none of these types of diagonals. For the diagonal distance across a square, use the Pythagorean Theorem a2 + b2 = c2, and find the variable c with a and b representing the different sides.

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