Question

the sum of any two sides of triangle is greater than the third side​

Answer 1

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Given: There is a triangle ABC.

To Prove: AB + AC> BC.

Construction: Extend BA to point D, so DA = CA. Join CD

=>Angle ADC = ACD

=>Angle BCD> ACD, so angle BCD> ADC (or BDC)

=>So in triangle DBC, line DB (or DA + AB)> BC

But line DA = AC, so lines AC + AB> BC.

(Henced Prove)

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Answer 2

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step-by-step explanation:

Let us consider a ∆ABC,

NOW,

Required To Prove : AB + AC> BC.

Foe this,

we shall do,

Construction : Extend BA to point D,

so that,

DA = CA

Now,

CD is joined.

Now,

=>Angle 1 = Angle 2

°.° angles opposite to equal sides are equal.

Clearly,

=>Angle BCD >Angle ACD

therefore,

Angle BCD > Angle ADC

( °.° Angle ACD = Angle ADC )

So,

in ∆DBC,

DB > BC

=> BA + AD > BC

( °.° DB = BA + AD )

But,

DA = AC

So,

AC + AB> BC.

Hence,

Proved...