# Using vector operations, Prove the line segment joining the midpoints of two sides of a triangle

Show, using vector operations, that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and has half its length.

## 1 Answer

Say vertices are A,B,C. Midpoint of AB is given by $$(A+B)/2$$. Midpoint of BC is given by $$(B+C)/2$$. So the vector joining these midpoints is $$(A+B)/2-(B+C)/2=(A-C)/2$$, i.e. is parallel to the vector $$A-C$$ and has half its length.