Stewart’s TheoremLayanah Nsouli, Kathy Chen, Artur Chojecki, and Jason Lee

Stewart’s Theorem

• Given ∆ ABC• Sides a b c are opposite the

vertices respectively• CP is drawn, it is called the

cevian• AP is equal to m and PB is

equal to n ( m + n = c )

Stewart’s Theorem Variables

Stewart’s Theorem Explained

Given a triangle , let cevian CP be drawn. Then label AP as m and PB as n. Then label the entire side AB as c. Now, Stewart’s Theorem states that ma2 + nb2 = (m+n) PC2 + mn2 + nm2. So, you would plug in then values that were given to you already in the formula, and then solve it for whatever is missing.

Uses

• This theorem is mainly used in geometric proof’s in order to prove that triangles are similar. When doing the proof, you use the parts of the formula as your reasons.

• You are usually trying to find the measure of the cevian.

• So, you plug in the variables that are given to you, and solve the equation step by step like explained above.

Example #1 In triangle ABC, AB=4, AC=6, AD=5 where D is the midpoint of BC.

Determine BC.

Example #2 In triangle ABC, AC=12, AD=10, and AB=8. Point D is a midpoint of

line CB. Determine the length of BD.

Example # 3 In triangle ABC, AC=10, CD= , and CB=20. Determine the length

of AB to the nearest whole number.

[Not drawn to Scale]