Question

In Fig. 6.63, D is a point on side BC of A ABC
BD
AB
such that
Prove that AD is the
CD
AC
B
bisector of Z BAC.​

Answer 1

Answer:

6.63 the point on the side BC of ABC ABC such that

Answer 2

Answer:

Given: ABC is a triangle and D is a point on BC such that

To prove: AD is the internal bisector of BAC.

Construction: Produce BA to E such that AE = AC. Join CE.

Proof: In AEC, since AE = AC

AEC = ACE ……….(i)

[Angles opposite to equal side of a triangle are equal]

Now, [Given]

[ AE = AC, by construction]

By converse of Basic Proportionality Theorem,

DA CE

Now, since CA is a transversal,

BAD = AEC ……….(ii) [Corresponding s]

And DAC = ACE ……….(iii) [Alternate s]

Also AEC = ACE [From eq. (i)]

Hence, BAD = DAC [From eq. (ii) and (iii)]

Thus, AD bisects BAC internally.