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Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

$$

\begin{aligned} \overrightarrow{M N} &=\overrightarrow{M B}+\overrightarrow{B N} \\ &=\frac{1}{2} \overrightarrow{A B}+\frac{1}{2} \overrightarrow{B C} \\ &=\frac{1}{2}(\overrightarrow{A B}+\overrightarrow{B C}) \\ &=\frac{1}{2} \overrightarrow{A C} \end{aligned}

$$

Vectors

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Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

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