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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