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

Question

In Fig. 6.63, D is a point on side BC of &#x394; ABC such that Prove that AD is thebisector of &#x2220; BAC

Philoid · Accepted Answer

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