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What is a quadrilateral?
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Quadrilateral just means "four sides", (quad means four, lateral means side).

Properties of a quadrilateralEdit

  • Four sides (or edges)


  • Four vertices (or corners).


  • The interior angles add up to 360 degrees:

Types of quadrilateral and their propertiesEdit

Rectangle-real-life-pic
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The Rectangle
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A rectangle is a four-sided shape where every angle is a right angle (90°).

Also opposite sides are parallel and of equal length.

Quadrilateral-rectangle
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Properties:

         Opposite sides are parallel

        Opposite sides are equal.

                All four angles are right angle.

Ø         Diagonal bisect each other.

Ø       Diagonals are equal in length.

Ø       Two pairs of congruent triangle are formed by the diagonal.

 

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The Rhombus
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A rhombus is a four-sided shape where all sides have equal length.

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Ø  Also opposite sides are parallel.

Ø  Opposite angles are equal.

Ø  All four sides are equal.

Ø  Four congruent triangles are formed by the diagonals.

Ø  Diagonals bisect the angles at the vertices.

Ø  The diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

Square-real-life-pic
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The Square
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A square has equal sides and every angle is a right angle (90°)

Ø  Also opposite sides are parallel.

Ø  Four congruent triangles are formed by diagonals.

Ø  Diagonal bisect each other at right angle.

Ø  All four sides are equal.

Ø  All four angles are right angle.

Ø  Diagonals are equal in length.

Ø  Diagonals bisect the angles at the vertices. Hence each angle is equal to 45 degree.

 

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Parallelogram-real-life-pic
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The Parallelogram
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A parallelogram's opposite sides are parallel and equal in length. Also opposite angles are equal (angles "a" are the same, and angles "b" are the same)

NOTE: Squares, Rectangles and Rhombuses are all Parallelogram

Properties:

Ø  Opposite sides are parallel.

Ø  Diagonal bisect each other.

Ø  Two pairs of congruent triangles are formed by diagonal.

Ø  Diagonal bisect each other.

Ø  Opposite angles are equal.

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The Trapezium
Trapezium
trapezium
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A trapezium (called a trapezium in the UK) has a pair of opposite sides parallel.

It is called an isosceles trapezium if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown.

A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides.

Properties of trapezium:

Ø  Only one pair of opposite sides parallel.

Property of isosceles trapezium:

Ø  One pair of opposite side parallel.

Ø  Pair of non-parallel sides is equal.

Ø  Two pairs of equal adjacent angles.

Quadrilateral-kite
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The kite
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Properties:

 It has two pairs of sides.

Ø  Each pair is made up of adjacent sides that are equal in length.  

Ø  The angles are equal where the pairs meet.

Ø  Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

 Quadrilateral Videos

PROPERTIES OF QUADRILATERALS (ANIMATION)(04:44)
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Quadrilateral Properties(05:07)
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