 What You'll Learn?

Before we get into the different types of quadrilaterals, let’s define what a quadrilateral is? what are the properties of it and also the properties of the types of quadrilaterals?

A quadrilateral is a simple closed figure bounded by four line segments in a plane.

The quadrilateral ABCD has four sides AB, BC, CD, and DA, four vertices are A, B, C, and D. ∠A, ∠B, ∠C, and ∠D are the four angles formed at the vertices.

When we join the opposite vertices A, C, and B, D. AC and BD are the two diagonals of the quadrilateral ABCD.

There are four angles in the interior of a quadrilateral. Can we find the sum of these four angles? Let us recall the angle sum property of a triangle. We can use this property in finding the sum of four interior angles of a quadrilateral.

ABCD is a quadrilateral and AC is a diagonal. We know the sum of the three angles of ABC is,

∠CAB + ∠B+ ∠BCA = 180° ….(1) ( angle sum property of a triangle)

∠CAD+ ∠D+ ∠DCA = 180° ….(2)

Adding (1) and (2), we get

∠CAB + ∠B + ∠BCA + ∠CAD + ∠D+ ∠DCA = 180° + 180°

Since ∠CAB + ∠CAD = ∠A and ∠BCA + ∠DCA = ∠C

So, ∠A + ∠B + ∠C + ∠D = 360°

i.e; the sum of four angles of a quadrilateral is 360° or 4 right angles.

Now let’s get into 6 differents:

1. Parallelogram
2. Square
3. Rectangle
4. Rhombus
5. Trapezium
6. Kite

### Parallelogram :

• A quadrilateral with both pairs of opposite sides are parallel and equal
• Opposite angles are equal
• Diagonals bisect each other.
• The Sum of adjacent angles is 180° ### Square:

• All sides are equal.
• All angles are equal of measure 90°
• Opposite sides are parallel to each other.
• Both diagonals are equal and bisect each other.
• Diagonals are perpendicular to each other. ### Rectangle:

• Opposite sides are equal.
• Adjacent sides are perpendicular to each other.
• All angles are equal and of measure 90°
• Both diagonals are equal and bisect each other.
• Opposite sides are parallel to each other. ### Rhombus :

• All sides are equal.
• Opposite angles are equal.
• Diagonals bisect and perpendicular to each other.
• The sum of the adjacent angles is 180°
• Opposite sides are parallel to each other. ### Trapezium:

• One pair of opposite side are parallel to each other. ### Kite :

• Two pairs of consecutive sides are equal.
• Diagonals are perpendicular to each other.
• One of the diagonal bisect each other. 