Question

Find the inverse of the statement, “If $\Delta ABC\,\,$ is equilateral, then it is isosceles”.
(a) If $\Delta ABC\,\,$ is isosceles, then it is equilateral.
(b) If $\Delta ABC\,\,$ is not equilateral, then it is isosceles.
(c) If $\Delta ABC\,\,$ is not equilateral, then it is not isosceles.
(d) If $\Delta ABC\,\,$ is not isosceles, then it is not equilateral.

Answer 1

Hint: To form the inverse of the given statement we have to just take the opposite of both the hypothesis and the result. We will check every option one by one and then see which is the correct option.

Complete step-by-step answer:
The inverse of the given statement is formed by taking the negation of both the hypothesis and the conclusion.
Here in the given question hypothesis is equilateral so negation of this is not equilateral and conclusion is isosceles so negation of this is not isosceles.
Let’s begin our inspection with option (a) If $\Delta ABC\,\,$ is isosceles, then it is equilateral. So according to the above definition this is not the correct option.
Now let’s move to option (b) If $\Delta ABC\,\,$ is not equilateral, then it is isosceles. So according to the above definition this is also not the correct option.
We will now move to option (c) If $\Delta ABC\,\,$ is not equilateral, then it is not isosceles. So according to the above definition this is the correct option.
Now let’s check option (d) If $\Delta ABC\,\,$ is not isosceles, then it is not equilateral. Hence this is also not the right answer according to the above definition.
Hence the answer is option (c).

Note: Understanding the concept of inverse of the statement is the key here and chances of mistakes are when we in a hurry may think option (b) as the correct option because we may think that the opposite of equilateral can be isosceles and vice-versa.