The sum of the lengths of any two sides of a triangle is _____________

1.	The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.a. doubleb. halfc. greater thand. less thanthe 2 people give answer who will explain get brainiest
Answer» ANSWER: Greater than 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.

The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.a. doubleb. halfc. greater thand. less thanthe 2 people give answer who will explain get brainiest

Answer»

Greater than

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.