Answer
See explanation
Work Step by Step
Examine the attached figure to convince yourself that this is true. Algebraically we can see that if the sides of the triangles are represented by the vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{a-b}$, then the segment going from the midpoint of $\mathbf{a}$ to the midpoint of $\mathbf{b}$ can be represented by the vector $\frac{1}{2}\mathbf{a}-\frac{1}{2}\mathbf{b}$. This vector has the same direction as $\mathbf{a}-\mathbf{b}$ and so they are parallel.
