Given: △klm, ks - angle bisector prove: km> sm

See below

Step-by-step explanation:

∠KSM = ∠SKL + ∠KLS . . . . . external angle is the sum of opposite internal angles

In order for SM > KM (in contradiction to the hypothesis), we must have

∠MKS > ∠KSM . . . . . . . . . . . angle measures are in the same order as opposite side measures

However, ∠MKS ≅ ∠SKL (given), so SM > KM requires ...

... ∠SKL > ∠SKL + ∠KLS

For any triangle with non-zero area, ∠KLS > 0, so the above statement will be false (a contradiction)

Negating the hypothesis results in a contradiction, so we conclude the hypothesis is true: KM > SM.