We will discuss here about Conditions for classification of quadrilaterals and parallelograms.

On the basis of the above definitions, theorems and converse propositions we conclude the following.

**1.** A quadrilateral is a parallelogram if any one of the
following holds.

(i) Each pair of opposite sides are parallel.

(ii) Each pair of opposite sides are equal.

(iii) Each pair of opposite angles are equal.

(iv) Diagonals bisect each other.

(v) One pair of opposite sides are parallel and equal.

**2.** A quadrilateral is a trapezium if one pair of its opposite sides are parallel.

3. A parallelogram is a

(i) rhombus if its diagonals interest at right angles.

(ii) rectangle if its diagonals are equal.

(iii) square if its diagonals are equal and intersect at right angles.

**Note:**

• Parallelograms, trapeziums, rhombuses, rectangles and squares are all quadrilaterals.

• Rhombuses, rectangles and squares are all parallelograms.

• All squares are rhombuses, but the converse is not true.

• All squares are rectangles, but the converse is not true.

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