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

• Four Sides (Tetragon)
• Four Vertices
• Interior angles’ sum to 360°
• Exterior angles’ sum to 360°

## Important Terms Related to Quadrilaterals

### Diagonals

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

• A quadrilateral can have only two diagonals

In the figure below line segment AD represents a diagonal of the Quadrilateral ABCD.

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

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

• DC and BC
• BC and AB

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

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

• ∠1 and ∠3
• ∠3 and ∠4
• ∠2 and ∠4
• ∠1 and ∠2

All interior angles are strictly less than 180 degrees

#### 1. Parallelogram

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

##### Properties of Parallelogram
• Theorem: Opposite sides are equal.
• Theorem: Opposite angels are equal.
• Theorem: Diagonals bisect each other.
• Theorem: The diagonals of a parallelogram bisect each other to form two pairs of congruent triangles.
• In a parallelogram if one angle is right angle, then all angles are right angle(i.e., It is a square).
• Theorem: Parallelograms on the same base and between the same parallels are equal in area.

#### 2. Rhombus (Rhomb)

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

##### Properties of Rhombus
• All four sides are equal in length
• Opposite sides are parallel(i.e., It’s a parallelogram).
• Opposite angles are equal
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• Diagonals are perpendicular bisectors of one another.
• In case, if one angle is right angle, then all angles are right angle(i.e., It will be a square).
• Four congruent triangles are formed by diagonals.

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

##### Properties of Rectangle
• Opposite sides that are equal and parallel (i.e., It’s a parallelogram).
• Adjacent sides are of unequal length
• Consecutive angles are supplementary (180 degree)
• Diagonals are equal and bisect each other.

A square is a rhombus whose all angles are right angles

##### Properties of Square
• The diagonals are equal and bisect each other and at right angle
• Opposite sides are parallel
• All four angles are equal
• All four sides are equal.

#### 5. Kite

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

##### Properties of Kites
• Two disjoint pairs of adjacent sides are equal (by definition)
• One diagonal is the perpendicular bisector of the other diagonal.
• One diagonal is a line of symmetry (it divides the quadrilateral into two congruent triangles that are mirror images of each other).
• One diagonal bisects a pair of opposite angles

#### 6. Trapezoid (Trapezium)

A quadrilateral with at least one pair of parallel sides is known as a trapezoid

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

At least one angle with a measure in between 180 degrees and 360 degrees

A cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle

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

## Angle Sum Property of a Quadrilateral

The sum of the angles of a quadrilateral is 360°