Question

By giving a counter example, show that the following statement is not true.
p : "If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle".

Answer 1

The given statement is of the form "if q, then r".

q: All the angles of a triangle are equal.

r: The triangle is an obtuse-angled triangle.

Statement p has to be proved false.
For this purpose, we need to prove that if q, then ~r.

To show this, none of the angles of the triangle should be obtuse.

We know that the sum of all angles of a triangle is 180°. Therefore, if all three angles are equal, then each of them will measure 60°, which is not an obtuse angle.

In an equilateral triangle, the measure of all angles is equal. Thus, the triangle is not an obtuse-angled triangle.

Hence, it can be concluded that statement p is false.