Question

prove that sum of any two sides of a triangle is greater than to third side​

Answer 1

Given triangle ABC,

extend BA to D such that AD = AC. Now in ΔDBC ∠ADC = ∠ACD [Angles opposite to equal sides are equal] Hence ∠BCD > ∠ BDC That is BD > BC [The side opposite to the larger (greater) angle is longer] Þ AB + AD > BC ∴ AB + AC > BC [Since AD = AC) Thus sum of two sides of a triangle is always greater than third side.

Answer 2

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. For example:-