Question

Which of the following is not true?
A. Equilateral triangle is a regular polygon.
B. Square is a regular polygon
C. Rectangle is a regular polygon
D. A regular polygon is both equiangular and equilateral.

Answer 1

Hint: In this question, we have to choose the incorrect statement. So we will first try to understand the definition and properties of a regular polygon and then we will compare it with all the other dimensional figures. We will also draw the diagram of a regular polygon to understand it better.

Complete answer:
We know that a polygon that has all the sides equal are all regular polygons. Since all the sides of a regular polygon are equal therefore we can say that all the angles are also equal.
Therefore we can say that a regular polygon is that which is equiangular i.e. all angles are equal in measure and equilateral which means that all the sides are of equal length.
Now from the above given options, we know that an equilateral triangle has all the sides equal and their angles are also equal. So this satisfies the properties of a regular polygon.
Now we have a square, again we know that all the sides and angles of a square are equal . therefore it is also a regular polygon.
The fourth option which is given is itself one of the major properties of a regular polygon.
Now we can see that a rectangle only shares one of the properties of a regular polygon i.e. it has equal angles but all the sides are not equal .
So the given statement is incorrect.

Therefore, the correct option is C

Note: We should note that the most common examples of a regular polygon are rhombus, square etc.
We should know that all the angles of an equilateral triangle are $60^\circ $ while all the equal angles of a square are $90^\circ $ .
The diagram of a regular polygon with $6$ sides is as below:

We should know that the formula of calculating the angle of a regular polygon of $n$ sides is:
$\dfrac{{(2n - 4)}}{n} \times 90^\circ $