  Written by
Malcolm McKinsey
Fact-checked by
Paul Mazzola

quadrilateral is a plane figure made with four line segments closing in a space. Quadrilaterals can be convex or concave and simple or complex. The easiest, fastest way to learn about quadrilaterals is to build one yourself. Find four straight objects to use as line segments (four = quad; side = lateral). If you connect the four linear objects at their eight ends, you have a quadrilateral, a four-sided polygon.

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Quadrilaterals appear in four different classifications:

1. Convex – Each interior angle is less than 180° and the two diagonals are inside the closed space of the quadrilateral.

2. Concave – One interior angle is greater than 180° and one diagonal lies outside the shape.

3. Simple – The quadrilateral does not cross its sides (it is not self-intersecting).

4. Complex – The quadrilateral has self-intersecting sides.

A quadrilateral has two identifying properties:

1. Four straight sides

2. Four vertices (angles where sides meet at their endpoints)

### How many sides does a quadrilateral have?

A quadrilateral has 4 straight sides. Sides and angles can be equal or unequal. When two or four sides are equal, you get special types of quadrilaterals such as trapezoids and rectangles.

All the other four-sided plane figures derive from the quadrilateral:

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• Rhombus

• Square

• Rectangle

• Parallelogram

• Kite

• Dart

• Trapezoid

## How to draw a quadrilateral

Use a straightedge or ruler to draw a quadrilateral. Draw four line segments so each endpoint touches one other endpoint. Whether you have drawn a simple or complex, convex or concave quadrilateral, you did it correctly!

Draw a simple quadrilateral. Do not let any line segments cross each other. Your simple quadrilateral could be either concave or convex. If two sides point inward, you drew a concave quadrilateral.

Now draw a quadrilateral where two non-adjacent line segments cross each other. You have drawn a complex quadrilateral.

Each vertex is given a letter, moving in either direction (clockwise or counterclockwise) to the next vertex, like quadrilateral ABCD. Each side of the quadrilateral is then identified by its line segment (ABBCCDDA). Each interior angle uses its vertex letter (∠A∠B∠C∠D).

### How to name a quadrilateral

A simple quadrilateral is also called a quadrangle or a tetragon. A simple quadrilateral will be symmetrical if it has at least one pair of congruent sides.

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• For a simple quadrilateral, interior angles of the four vertices add to 360°.

• For a convex quadrilateral, each interior angle will be less than 180°.

• For a concave quadrilateral, one interior angle will be greater than 180°.

• For a complex quadrilateral, interior angles add to 720° because two of the interior angles are reflex angles, each greater than 180° but less than 360°.

All convex quadrilaterals have diagonals (line segments connecting non-adjacent vertices) inside their enclosed space.

All concave quadrilaterals have one of their diagonals outside their enclosed space. All complex quadrilaterals have both diagonals outside their enclosed space.