Question

Provethat AD is angle bisector in thebfigure.

Given is:-∟ABC=∟ACB=68 ,∟ADB=100​

Answer 1

In ΔABC ,

AC>AB (given)

So,

∠B>∠C ............... (1) ( Angle opposite to the larger side is Larger )

In ΔABD,

∠1+∠B+∠ADB=180°

∠B=180°

−∠1−∠ADB .................... (2)

In ΔADC,

∠2+∠C+∠ADC=180°

∠C=180°

−∠2−∠ADC .................... (3)

From (1), (2) and (3)

180 °

−∠1−∠ADB>180°

−∠2−∠ADC

180°

−∠1−∠ADB>180°

−∠1−∠ADC ( ∠1=∠2 )

−∠ADB>−∠ADC

⇒∠ADB<∠ADC

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