Can the diffference of two sides of a triangle be equal to less than a third side?
The difference between two sides of a triangle will always be less than the third side.Let ABC be a triangle where AC > AB, extend side AB to point D so that AD = AB + (AC-AB) = AC. Therefore, since AC = AD, triangle ADC is a isosceles where angles ADC and ACD are equal.In the triangle BCD, angle BCD < BDC, Since, angles BCD is part of angle ACD (ACB + BCD ) and angle ACD is equal to BDC .Therefore, using the knowledge that, in a triangle, side opposite a greater angle is always greater than the side opposite a smaller angle, it is proved that, the difference between two sides is always lesser than the third side.In an isosceles, the difference of two sides is zero, since the sides are equal. The third side would always be greater than zero to form a triangle. The same logic can be applied to an equilateral triangle.