Question

PROVE COVERSE OF ANGLE BISECTOR PROPERTY.......

Answer 1

Given: ABC is a △ ; AD divides BC in the ratio of the sides containing the

angles ∠A to meet BC at D.

i.e. AB/AC = BD/DC 

To prove: AD bisects ∠A.

Construction: Draw CE || DA to meet BA produced at E

Proof: In △ABC. CE || DA cut by AE

∠BAD = ∠AEC (corresponding angle) -(i)

Similarly CE || DA cut by AC

∠DAC = ∠ACE (alternate angles) -(ii)

In △BEC; CE || AD

AB = BD (BPT) 

AE = DC

But AB = BD (given)

AC = DC

AB = AB

AE = AC

AE = AC

⇒∠AEC = ∠ACE (isosceles property ....(iii)

According to equation (i),(ii)and(iii)∠BAD = ∠DAC

⇒ AD bisects ∠A.

Thanx

Answer 2

ones you see in 9 std 13 chapter of math

geometrical construction chapter and you will get this answer by reading all the properties.