Q9 of 65 Page 152

In Fig. 6.63, D is a point on side BC of Δ ABC such thatProve that AD is thebisector of ∠ BAC

Construct a line CM which meets BA extended up to AM so that AM = AC

This means, ∠AMC = ∠ACM (Angles opposite to equal sides)


(Given)



BECAUSE AM = AC


Hence,


ΔABD ΔMBC


Hence, AD parallel MC


This means,


∠DAC = ∠ACM (Alternate angles)


Since,


∠AMC = ∠ACM


Hence,


∠DAC = ∠BDA


Hence, AD is the bisector of ∠BAC


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