Which of these is NOT necessarily a parallelogram?

Class 9QuadrilateralsGeometry — Quadrilaterals

AA quadrilateral with both pairs of opposite sides equal
BA quadrilateral with both pairs of opposite angles equal
CA quadrilateral with one pair of sides parallel
DA quadrilateral with diagonals bisecting each other

Step-by-Step Solution

One pair of parallel sides → trapezium (could be a parallelogram, but not necessarily). The other three are valid parallelogram tests.

Answer: C) A quadrilateral with one pair of sides parallel

Key idea: Tests for a parallelogram

A quadrilateral is a parallelogram if ANY ONE of the following is true:

- Both pairs of opposite sides are parallel (definition).
- Both pairs of opposite sides are equal.
- Both pairs of opposite angles are equal.
- Diagonals bisect each other.
- One pair of opposite sides is **both equal AND parallel**.

That last one is the most efficient — only ONE pair to check, but you need both 'equal' AND 'parallel'.

Don't confuse: just 'one pair parallel' is a trapezium, not a parallelogram.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Quadrilaterals practice questions

More Class 9 Quadrilaterals practice

Which special parallelogram is described by the property: 'Diagonals are equal but NOT…Joining the midpoints of the sides of a rectangle in order gives a ____.In ΔABC, D is midpoint of AB. A line through D parallel to BC meets AC at E. If AC = 10…In a rhombus, the diagonals are 16 cm and 12 cm. Find the side length.How many diagonals does a quadrilateral have?