# <span lang="EN-US

Given: In ∆ABC, BD=BC and B=60° and A=70°

Proof:

In ∆ABC, by the angle sum property, we have

A + B + C = 180°

70° + 60° + C = 180°

130° + C = 180°

C = 50°

Now in ∆BCD we have,

CBD = DAC + ACB … as CBD is the exterior angle of ABC

= 70° + 50°

Since BC = BD …given

So, BCD = BDC

BCD + BDC = 180° - CBD

= 180° - 120° = 60°

2BCD = 60°

BCD = BDC = 30°

Now in ∆ACD we have

A = 70°, D = 30°

And ACD = ACB + BCD

= 50° + 30° = 80°

∴∠ACD is greatest angle

So, the side opposite to largest angle is longest, ie AD is longest side.

Since, BDC is smallest angle,

The side opposite to BDC, ie AC, is the shortest side in ACD.

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