#### A quadrilateral is a polygon with four sides (edges) or four vertices or four corners it can also be called as a TETRAGON

There are different types and varieties of quadrilaterals having different properties such as different angles and sides. You can learn them here in a very easy and informative way.

## And at last but not the least all types and properties of parallelogram, rhombus, square, rectangle, kite, oblong, trapezoid, etc.

-Four sides.
-Four vertices (corners).
-Interior angles sum to 360°.
-Exterior angles sum to 360°.

## Important Terms Related to Quadrilateral:

### Diagonals:-

Diagonals are line segments that join two opposite vertices of a quadrilateral (corners).

A quadrilateral can have maximum two diagonal

Where AD is the line segment joining two opposite vertices A and D

Two sides are adjacent, if they share a common vertex.

In the quadrilateral shown above the 4 pair of adjacent sides are:

2.  DC and BC
3.  BC and AB

Two angles are adjacent, if they share a common side.

In the quadrilateral shown above the 4 pair of adjacent angles are:

1. ∠1 and ∠3
2. ∠3 and ∠4
3. ∠2 and ∠4
4. ∠1 and ∠2

There are special types of quadrilateral:

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

A quadrilateral that contains a reflex angle.

#### 1. Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel and equal sides

#### Properties of Parallelogram :-

• Opposite sides are congruent(i.e., Equal in length).
• Opposite angels are congruent(i.e., Equal in length).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• The diagonals of a parallelogram bisect each other to form two pairs of congruent triangles.

#### 2. Rhombus (Rhomb) {Equilateral Quadrangle

A rhombus is a parallelogram all of whose all four sides are congruent

#### Properties of Rhombus :-

• All four sides are congruent(i.e., Equal in length).
• Opposite sides are parallel(i.e., It’s a parallelogram).
• Opposite angels are congruent(i.e., Equal in length).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• The diagonals of a rhombus bisect pairs of opposite angles.
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• Four congruent triangles are formed by diagonals.

#### 3. Rhomboid

A rhomboid is a parallelogram in which adjacent sides are of unequal lengths and oblique angles

#### Properties of Rhomboid :-

• All four sides are congruent(i.e., Equal in length).
• Opposite angels are congruent(i.e., Equal in length).
• Opposite angels are parallel(i.e., It’s a parallelogram).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• The diagonals bisect each other to form two pairs of congruent triangles.

A rectangle is a plane figure with four straight sides and four right angles

Properties of Rhombus :-

• Opposite sides that are congruent and parallel.
• Adjacent sides are of unequal length
• Consecutive angles are supplementary, and
• Diagonals bisect each other.

A square is a rhombus whose all angles are right angles

#### Properties of Square :-

• The diagonals bisect each other and at right angle.
• The diagonals bisect its angles.
• Opposite sides parallel and congruent.
• All four angles square are congruent.
• All four sides square are congruent.
• The diagonals are congruent.

#### 6. Oblong

A oblong is a rectangle which has unequal adjacent sides.

#### Properties of oblong :-

• Two sets of parallel lines meeting at right angles.

#### 7. Kite

A kite is a quadrilateral whose two pair of adjacent sides are equal

#### Properties of Kites:-

• Two sets of parallel lines meeting at right angles.
• Two disjoint pairs of consecutive sides are congruent by definition   Note: Disjoint means that the two pairs are totally separate.
• The diagonals are perpendicular.
• One diagonal is the perpendicular bisector of the other diagonal
• The main diagonal bisects a pair of opposite angles.
• The opposite angles at the endpoints of the cross diagonal are congruent.

#### Properties of Kites:-

• The bases are parallel by definition.
• Each lower base angle is supplementary to the upper base angle on the same side.

A cyclic quadrilateral (inscribed quadrilateral) is a quadrilateral drawn inside a circle so that its corners lie on the circumference of the circle

whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle.

(a) the opposite angles of a cyclic quadrilateral sum to 180°
i.e. a+ c = 180°
b + d = 180°
(b) the exterior angle of a cyclic quadrilateral is equal to the interior
opposite angle

i.e. e = c

Summary
Here is a list of all the properties of quadrilaterals that we have mentioned along with the classes of the quadrilaterals that possess those properties:
 Property Quadrilaterals Orthodiagonal Kite, Dart, Rhombus, Square Cyclic Square, Rectangle, Isosceles Trapezoid Inscriptible Kite, Dart, Rhombus, Square Having two parallel sides Rhombus, Square, Rectangle, Parallelogram, Trapezoid Having two pairs of parallel sides Rhombus, Square, Rectangle, Parallelogram Equilateral Rhombus, Square Equiangular Rectangle, Square