Question

Prove that The sum of any two sides of a triangle is greater than the third side.​

Answer 1

Step-by-step explanation:

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.

Answer 2

Answer:

∠ABD>∠CDB. Hence we have AD>AB( because the side opposite to a larger angle is longer). AD = AC+BC. Hence thesum of two sides of a triangle is largerthan the third side.