Question

The number of lines of symmetry in a trapezium is
A.Infinite
B.$2$
C.$3$
D.None

Answer 1

Hint: To answer this question, we would draw two types of trapezium, a proper trapezium and an isosceles trapezium. Now, we would try to make a line of symmetry such that it divides the trapeziums in two equal parts. Hence, to answer this question, we would consider a proper trapezium rather than the isosceles one as it is not important that every time the opposite sides are equal as in the case of isosceles one, hence, we would reach our desired answer.

Complete step-by-step answer:
Before answering this question, we should know what exactly a trapezium is.
Hence, a trapezium is a four sided, two-dimensional shape having two of its sides parallel to each other.
Now, to answer this question, we would consider two types of trapeziums i.e. a regular trapezium and an isosceles trapezium.
Regular Trapezium:
A regular trapezium or also known as a proper trapezium is a trapezium having one pair of opposite sides parallel but the other two sides need not be equal to each other.

Now, when a shape is folded and it sits completely on the top of itself, then the fold line is called a line of symmetry.
As from the above figure, clearly, a proper trapezium does not give any line of symmetry. Hence, a proper trapezium has no line of symmetry.
Isosceles Trapezium:
Isosceles trapeziums are those trapeziums having one pair of opposite sides parallel and the other pair of opposite sides equal. They are just like isosceles triangles.
Now, when we try to fold them vertically, then the shape completely sits on top of itself and joins all the edges. Hence, we would get a line of symmetry.

Hence, we can say that proper trapezium does not have any line of symmetry but an isosceles trapezium has one line of symmetry which passes through the mid-point of the two opposite parallel lines.
Hence, a trapezium can have utmost 1 line of symmetry.
Therefore,
The number of lines of symmetry in a trapezium is 0 as the opposite sides need not be equal to each other.
Hence, option D is the correct answer.

Note: We should know what exactly a proper trapezium is and how it looks like before solving these types of questions. Also, we would consider a proper trapezium to answer this question as improper trapeziums such as parallelograms, rectangles, squares, etc. have a pair of parallel sides but they can have more than one line of symmetry. This question is completely concept based and hence, it is important.