Questions & Answers
Question
Answers

State true or false.
Every parallelogram is a trapezium.
$
  {\text{A}}{\text{. True}} \\
  {\text{B}}{\text{. False}} \\
$

Answer Verified Verified
Hint:-In this question first we need to analyse the parallelogram and its properties. Then analyse the trapezium and its properties and finally check that every property of parallelogram is also the property of trapezium or not.

Complete step-by-step answer::
We know, a parallelogram is a special type of quadrilateral that has equal and parallel opposite sides.
The given figure shows a parallelogram ABCD which has AB parallel to CD and AD parallel to BC.
Also, AD=BC
And AB=CD

And the trapezium is a quadrilateral, which is defined as a shape with four sides and one set of parallel sides.
The given figure shows a trapezium ABCD which has AB side parallel to CD and two other sides AD and BC which are non-parallel.
$
   \Rightarrow {\text{AB = CD}} \\
  {\text{and AD = BC}} \\
 $

From the above discussion, we observe that the pair of opposite sides of a parallelogram are equal and parallel but in the case of trapezium, this is not true in that only one pair of opposite sides are equal.
Therefore every parallelogram is not a trapezium.
Hence, option B. is correct.

Note:- Whenever you get this type of question the key concept to solve this is to learn about different shapes like quadrilateral, rectangle, square, parallelogram, trapezium, rhombus and their properties.