Given a triangle with sides of length opposite vertices are , , , respectively. If cevian is drawn so that , and , we have that . (This is also often written , a form which invites mnemonic memorization, i.e. "A man and his dad put a bomb in the sink.")
Setting the two left-hand sides equal and clearing denominators, we arrive at the equation: . However, so and This simplifies our equation to yield or Stewart's theorem.
Proof 2 (Pythagorean Theorem)
Applying Pythagorean on yields
Substituting , , and in and gives
are equal to each other. Thus, Rearranging the equation gives Stewart's Theorem:
Nearly Identical Video Proof with an Example by TheBeautyofMath