What is the inverse of the following statement? if ∆abc is equilateral, then it is isosceles. if ∆abc is equilateral, then it is isosceles. if ∆abc is not isosceles, then it is not equilateral. if ∆abc is not equilateral, then it is not isosceles. if ∆abc is isosceles, then it is equilateral.

We have to find the inverse of the given statement:

" If ∆ABC is equilateral, then it is isosceles."

A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.

1. Consider the first option

" If ∆ABC is equilateral, then it is isosceles"

This statement is true but is not the inverse statement of the given statement.

2. Consider the second option

"If ∆ABC is not isosceles, then it is not equilateral."

If triangle ABC is not isosceles, it means the two sides of a triangle does not have an equal measure, which is quiet obvious that it will not be equilateral triangle. As to be an equilateral triangle, all the three sides should be of equal measure.

Therefore, it is the correct inverse statement of the given statement.

3. Consider the third option

"If ∆ABC is not equilateral, then it is not isosceles"

This is not necessarily true, if a triangle is not equilateral, it means that the three sides of a triangle does not have an equal measure. But still two sides of a triangle can still have equal measure. Therefore, it can be isosceles.

Therefore, it is not the correct inverse statement for the given statement.

4. Consider the fourth statement

"If ∆ABC is isosceles, then it is equilateral"

If a triangle is isosceles, it means that the two sides of a triangle have an equal measure. So, it can not be equilateral triangle.

Therefore, it is not the correct inverse statement for the given statement.

So, Option 2 is the correct answer.

could you provide figure.