By giving a counter example, show that the following statements are not true.

*p*: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

#### Solution

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.

The given statement *p* has to be proved false. For this purpose, it has to be proved that if *q*, then ∼*r*.

To show this, angles of a triangle are required such that none of them is an obtuse angle.

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

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

Thus, it can be concluded that the given statement *p* is false.