If a cevian of length t is drawn and divides side a into segments m and n, then
For this proof we will use the law of cosines and the identity .
Label the triangle with a cevian extending from onto , label that point . Let CA = n Let DB = m. Let AD = t. We can write two equations:
When we write everything in terms of we have:
Now we set the two equal and arrive at Stewart's theorem: