Question

In figure 3.61, bisector of ∠BAC intersects side BC at point D. Prove that AB>BD

Answer 1

SOLUTION:-
given by:- , bisector of ∠BAC intersects side BC at point D.
》enterior ∠ADB = ∠DAC + ∠ACD
》 = ∠BAD + ∠ACD
》 ∠ DAC = ∠BAD ( GIVEN)
》∠ADB = ∠BAD
》the side opposite to angle ∠ADB in the longest side in triangle ADB
》SO , AB > BD


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Answer 2

Given ,

<BAC intersects side BC at point D.

<DAC = <BAD ---( 1 )

Proof :

In ∆ADC , CD is extended to B.

exterior angle ADB > angle DAC

=> <ADB > angle BAD [ from ( 1 ) ]

AB > BD

[ Since ,

The sum of any two sides of a triangle

is greater than the third side . ]

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