CBSE Class 9 Answered

Given: The side BC of ABC is produced to D, the bisector of BAC intersects the side BC at E.

To prove: ABC + ACD = 2AEC

Proof:

We know that ACD = ABC + BAC … (1)

(ext. angle theorem)

AE is bisector of BAC, thus

i.e., BAC = 2BAE

Thus equation (1) reduce to

ACD = ABC + 2BAE

Adding ABC on both sides,

Now ABC + ACD = ABC + ABC + 2BAE

= 2 (ABC + BAE)

= 2 (AEC) [Ext angle of ABE]

Hence proved.