Question

Which of the following quadrilaterals is not a parallelogram?
A. Rectangle
B. Trapezium
C. Square
D. Rhombus

Answer 1

Hint: We write definition of each of the given quadrilaterals and write definition of a parallelogram. Check which of the given options contradicts the properties of a parallelogram.

Complete step by step answer:
We know a quadrilateral is a closed figure having four vertices (corners) and four edges (sides).
Now we write the definition of a parallelogram using the concept of a quadrilateral.
Parallelogram:
A parallelogram is a quadrilateral having the opposite pair of sides equal and parallel. The angles opposite to each other are equal in measure.
We write definitions of terms given in options.
Rectangle: A rectangle is a quadrilateral having all angles as right angles and opposite sides equal and parallel to each other.
\[ \Rightarrow \]A rectangle is a type of parallelogram.
Trapezium: A quadrilateral having one pair of opposite sides parallel is called a trapezium.
Since other pair of sides is not parallel to each other, then trapezium is not a kind of parallelogram
\[ \Rightarrow \]A trapezium is not a type of parallelogram.
Square: A square is a quadrilateral with all sides of equal length, all angles as right angles and opposite sides parallel to each other.
\[ \Rightarrow \]A square is a type of parallelogram.
Rhombus: A rhombus is a quadrilateral whose all sides are of equal length and opposite sides are parallel to each other. Opposite angles of rhombus are equal in measure.
\[ \Rightarrow \]A rhombus is a type of parallelogram.
A trapezium is the quadrilateral that is not a parallelogram as its two sides are not parallel.

\[\therefore \]Option B is correct.

Note: Many students make the mistake of choosing the option rhombus as they think rhombus is a quadrilateral with sides equal but they don’t need to be parallel. Keep in mind opposite sides are parallel in a rhombus, i.e. a rhombus is just tilted square.