Stewart’s Theorem Layanah Nsouli, Kathy Chen, Artur Chojecki, and Jason Lee.

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Stewart’s Theorem Layanah 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 ma 2 + nb 2 = (m+n) PC 2 + mn 2 + nm 2. 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]