Geometry: Quadrilaterals



In this lesson we will learn

  • quadrilaterals
  • types of quadrilaterals: parallelogram, rhombus, rectangle, square, trapezoid, kite, trapezium

Related Topics: More Geometry Lessons

Quadrilaterals

Quadrilaterals are two-dimensional four-sided polygons on a plane.

Quadrilaterals have the following properties

  • four sides
  • two diagonals
  • four internal angles (or vertices)
  • the interior angles add up to 360°

A convex quadrilateral has all angles less than 180º.
A concave quadrilateral has at least one angle greater than 180º. (memory tool: concave has a "cave" in it)


convex concave quadrilateral

Worksheet on Angles of Quadrilaterals

Types of Quadrilaterals

We will describe the following types of quadrilaterals: parallelogram, rhombus, rectangle, square, trapezoid, kite and trapezium.

Parallelogram

A parallelogram is a four-sided polygon that has the following properties

  • opposite sides are parallel
  • opposite sides are equal
  • opposite angles are equal
  • diagonals bisect each other
  • no line of symmetry
parallelogram parallelogram


Rhombus

A rhombus is a four-sided polygon that has the following properties

  • opposite sides are parallel
  • all four sides are equal
  • opposite angles are equal
  • diagonals bisect each other at right angles
  • two lines of symmetry (which are the diagonals)

A rhombus is a special case of a parallelogram with four equal sides.

rhombus rhombus


Rectangle

A rectangle is a four-sided polygon that has the following properties

  • opposite sides are parallel
  • opposite sides are equal
  • its angles are all right angles (i.e. 90º)
  • diagonals bisect each other
  • diagonals are equal
  • two lines of symmetry

A rectangle is a special case of a parallelogram with all angles equal to 90º

rectangle

rectangles



Square

A square is a four-sided polygon that has the following properties

  • opposite sides are parallel
  • all sides are equal
  • its angles are all right angles (i.e. 90º)
  • diagonals bisect each other at right angles
  • diagonals are equal
  • four lines of symmetry

A square is a special case of a rectangle in which all the sides are equal..

square

square

Take note that a diagonal of a square makes two 45º-45º-90º triangles with the sides of the square. Therefore, when given the length of a side, you will be able to work out the length of the diagonal. Or when given the length of the diagonal, you will be able to figure out the length of the side.



Trapezoid

There are two possible definitions for trapezoids.

A trapezoid is a four-sided polygon that has exactly one pair of opposite sides parallel. Using this definition, a parallelogram would not be considered a trapezoid.

A trapezoid is a four-sided polygon that has at least one pair of opposite sides parallel. Using this definition, a parallelogram is a special case of a trapezoid.

A trapezoid is also called a trapezium (UK English).

trapezoid 1 trapezoid 2
p is parallel to q l is parallel to m

An isosceles trapezoid has the following properties

  • the two non-parallel sides are equal in length
  • the base angles are equal

IsoscelesTrapezoid_900.gif

A right trapezoid is a trapezoid with two right angles.

TrapezoidRight





Kite

A kite is a four-sided polygon that has the following properties

  • two pairs of adjacent sides equal
  • one pair of opposite angles equal
  • longer diagonal bisects the shorter diagonal at right angles
  • one line of symmetry

kite



Trapezium

A trapezium represents a different shape depending on whether you are in the US or not.

In the US, a trapezium is a quadrilateral that has no parallel sides.
Outside the US, a quadrilateral that has no parallel sides is called an irregular quadrilateral.

Outside the US, a trapezium is a quadrilateral that has a pair of parallel sides.
In the US,
a quadrilateral that has a pair of parallel sides is called a trapezoid.

Worksheets on Properties of Quadrilaterals



Videos

The following video shows how to identify and classify quadrilaterals given some properties.



The following videos gives an overview of quadrilaterals.
Convex quadrilaterals, Concave Quadrilaterals, trapezoid, parallelograms, rectangles, rhombi and squares



Quadrilaterals: classifying and the sum of their angles.



Identify Special Quadrilaterals using a tree diagram





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