Question

Do you agree with the statement “In a triangle, the sum of any two sides is greater than the third side”? Justify your answer with relevant proof.
Pls answer this qiuck

Answer 1

A triangle can be drawn only when the sum of any two sides is greater than the third side. We know that in a triangle the sum of any two sides is greater than the third side.


Now, extend (or) produce BO to meet AC in D.
Given ΔABC, 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.