Question

18. Prove that any two sides of a triangle are together
greater than the third side.​

Answer 1

Answer:

Construction: In ΔABC, extend AB to D in such a way that AD=AC.

In ΔDBC, as the angles opposite to equal sides are always equal, so,

∠ADC=∠ACD

Therefore,

∠BCD>∠BDC

As the sides opposite to the greater angle is longer, so,

BD>BC

AB+AD>BC

Since AD=AC, then,

AB+AC>BC

Hence, sum of two sides of a triangle is always greater than the third side.