<P> Angles ∠ BAD and ∠ DAC are equal . Therefore, the right hand sides of equations (1) and (2) are equal, so their left hand sides must also be equal . </P> <Dl> <Dd> B D D C = A B A C, (\ displaystyle (\ frac (BD) (DC)) = (\ frac (AB) (AC)),) </Dd> </Dl> <Dd> B D D C = A B A C, (\ displaystyle (\ frac (BD) (DC)) = (\ frac (AB) (AC)),) </Dd> <P> which is the angle bisector theorem . </P>

If the bisector of an angle of a triangle