Convex & Concave Quadrilaterals: Definition, Properties & Examples

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Lesson Transcript
Instructor: David Karsner
Quadrilaterals are four sided polygons. This lesson defines and provides examples of both convex and concave quadrilaterals. Take a look at the quadrilateral, its sub-categories and their properties.

One great thing about understanding quadrilaterals is that they can be found pretty much everywhere. Look around the room that you are in right now and you can probably identify several quadrilaterals. For instance, someone might see an envelope that is a rectangle. Outside a window, an individual might see a street sign that is a square or the face of a rock that is a trapezoid. These polygons are seen in nature, in household objects, and maybe even in your own doodling that you draw on the edges of your notebook. Quadrilaterals are everywhere.

A quadrilateral is a polygon composed of four sides and four angles. 'Quad' in the word quadrilateral means four. The basic shapes that fall under the quadrilateral category include: square, rectangle, rhombus, parallelogram, trapezoid, and kite. The angles of these shapes will always have a sum of 360 degrees. The sides will always meet at endpoints. An endpoint in geometry is called a vertex. Once it is clear that all quadrilaterals have four sides, they can be further categorized as convex or concave.

A convex quadrilateral is a four sided polygon that has interior angles that measure less than 180 degrees each. The diagonals are contained entirely inside of these quadrilaterals. Convex quadrilaterals can be classified into several sub-categories based on their sides and angles. These are the common quadrilaterals that are seen every day and are taught to students at a very young age.

If a quadrilateral has two sets of parallel sides, it is classified as a parallelogram. Rectangles are parallelograms that have four right angles. A rhombus is a parallelogram that has four congruent sides. Congruent means that something is equal in size or shape. A rhombus with congruent sides could have sides that all measure four inches in length. A square is a parallelogram with four congruent angles (right angles) and four congruent sides, and it has all the properties of a parallelogram, rectangle, and a rhombus. Parallelograms are convex quadrilaterals.

If a quadrilateral has only one set of parallel sides, it is classified as a trapezoid. The two sides that are parallel are called bases and will not be congruent. An isosceles trapezoid has two sides, the bases, that are parallel and the other two sides are congruent, but not parallel. A trapezoid is a convex quadrilateral.

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