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## Trapezium:

A quadrilateral having **exactly one pair of parallel sides**, is called a trapezium.

ABCD is a trapezium in which **AB || DC.**

## Isosceles Trapezium:

A trapezium is said to be an isosceles trapezium, if its **non-parallel sides are equal.**

Thus, a quadrilateral ABCD is an isosceles trapezium, if

**AB || DC and AC = BD.**

The diagonals of an isosceles trapezium are always equal.

## Parallelogram:

A quadrilateral is a parallelogram if its **both pairs of opposite sides are parallel.**

Quadrilateral ABCD is a parallelogram, because

**AB || DC and AD || BC.**

### Parallelogram Properties:

1) The opposite sides of a parallelogram are equal and parallel.

2) The opposite angles of a parallelogram are equal.

3) The diagonals of a parallelogram bisect each other.

Thus, in a parallelogram ABCD, we have:

1) AB = DC, AD = BC and AB || DC, AD || BC.

2) \(\angle{BAD} = \angle{BCD}\) and \(\angle{ABC} = \angle{ADC}\).

3) If the diagonals AC and BD intersect at O, then OA = OC and OB = OD.

## Rhombus:

A parallelogram having **all sides equal** is called a rhombus.

Thus, a parallelogram ABCD is a rhombus if **AB = AD.**In other words, a quadrilateral ABCD is a rhombus if

**AB || DC, AD || BC and AB = BC = CD = DA.**

ABCD is a rhombus, since ABCD is a parallelogram in which AB = AD.

### Rhombus Properties:

1) The opposite sides of a rhombus are parallel.

2) All sides of a rhombus are equal.

3) The opposite angles of a rhombus are equal.

4) The diagonals of a rhombus bisect each other at right angles.

Thus, in a rhombus ABCD, we have:

1) AB || DC and AD || BC.

2) AB = BC = CD = DA.

3) \(\angle{DAB} = \angle{BCD}\) and \(\angle{ABC} = \angle{CDA}\).

4) Let the diagonals AC and BD intersect at O. Then, OA = OC. OB =O D and \(\angle{AOB} = \angle{COD}\) and \(\angle{BOC} = \angle{AOD} = 1 right angle\).

## Rectangle:

A parallelogram whose** each angle is a right angle**, is called a rectangle.

ABCD is a rectangle in which **AB || CD, AD || BC** and** \(\angle{A} = \angle{B} = \angle{C} = \angle{D}\) = 90°.**

### Rectangle Properties:

1) Opposite sides of a rectangle are equal and parallel.

2) Each angle of a rectangle is 90°.

3) Diagonals of a rectangle are equal.

Thus, In a rectangle ABCD, we have:

1) AB = DC, AD = BC and AB || DC, AD || BC.

2) \(\angle{A} = \angle{B}\) and \(\angle{C} = \angle{D} = 1 right angle\).

3) Diagonal AC = diagonal BD.

## Square:

A square is a rectangle with a **pair of adjacent sides equal.**

In other words, a parallelogram having

**all sides equal**and

**each angle equal to a right angle**, is called a square.

ABCD is a square in which **AB || DC, AD || BC, AB = BC = CD = DA** and** \(\angle{A} = \angle{B} = \angle{C} = \angle{D}\) = 90°.**

### Square Properties:

1) The sides of a square are all equal.

2) Each angle of a square is 90°.

3) The diagonals of a square are equal and bisect each other at right angles.

Thus, in a square ABCD, we have:

1) AB = BC = CD = DA.

2) \(\angle{A} = \angle{B}\) and \(\angle{C} = \angle{D}\) = 90°.

3) Diagonal AC = Diagonal BD.

## Kite:

A quadrilateral is a kite if it has **two pairs of equal adjacent sides** and **unequal opposite sides.**

Thus, a quadrilateral ABCD is a kite, if **AB = AD, BC = CD** but **\({AD}\neq{BC}\) and \({AB}\neq{CD}\).**