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By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.
By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.
RS Agarwal Maths Class 11 Mathematical Reasoning
By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

By the properties of triangles, if all the sides of a triangle are equal, then the
each of the angle of the triangle will also be equal.
By the question,
All sides of the triangle are equal.
∴ All angles of the triangle are also equal.
Let each angle of the equilateral triangle be x°. We know that the sum of all angles of a
triangle is 360°.
x° + x° + x° = 360°
→ 3x° = 360°
→ x° = (360 ÷ 3 )°
∴ x° = 60°
Thus, all angles of the triangle measure 60° which is an acute angle (lying between 0°
and 90°.)
Obtuse angles are those which lie between 90° and 180°.
Thus, when all sides are equal in a triangle, its angles measure 60° each. This implies
that all angles are acute angles and not obtuse angles.

Thus, the statement p is false.

 

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