Here we will discuss about the concept of parallelogram.

**Quadrilateral:** A rectilinear figure enclosed by four line
segments is called a quadrilateral. In the adjoining figures, we have two
quadrilaterals PQRS, each enclosed by four line segments PQ, QR, RS and SP
which are called the sides of the quadrilateral.

The point of intersection of any two consecutive sides is called a vertex. Here P, Q, R and S are the vertices. PR and QS are the two diagonals of the quadrilateral PQRS. In figure (i), the two diagonals cut each other internally at O. But in figure (ii), they cut each other externally at O when one of the diagonals is produced.

The quadrilateral in figure (i) is a convex quadrilateral, while in figure (ii), the quadrilateral is nonconvex. In a convex quadrilateral, each of the four angles, i.e., ∠QPS, ∠PQR, ∠QRS and ∠RSP as in figure (i), is less than 180°. But in a nonconvex quadrilateral, one of the four angles will be greater than 180°. In the above figure (ii), ∠PSR is greater than 180°.

**Parallelogram:** A quadrilateral whose opposite sides are
parallel, is called a parallelogram. In the given figure PQRS is a parallelogram
in which PQ ∥ SR and PS ∥ QR.

**Rectangle:** A parallelogram is called a rectangle if one of its
angle is a right angle. In the given figure PQRS is a rectangle. Here PS ∥ QR, PQ
∥ SR and ∠P = 90°.

Consequently all angles will be right-angle.

**Note:** Every rectangle is a parallelogram but the converse is
not true.

**Rhombus:** A quadrilateral whose all sides are equal, is called a
rhombus. In the given figure, PQ = QR = RS = SP. So, PQRS is a rhombus.

**Square:** A rhombus is called a square if its angles are right
angle. In the given figure, PQ = QR = RS = SP and ∠SPQ = ∠PQR = ∠QRS = ∠RSP =
90°. So, PQRS is a square.

**Trapezium:** A quadrilateral whose one pair of opposite sides are
parallel, is called a trapezium. In the given figure, PQRS is a trapezium in which PQ ∥ SR and PS, QR are
its oblique sides. If the oblique sides PS , QR are equal, the trapezium is
called isosceles trapezium.

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