Theorem 10.1.3

Theorem: The line segment joining the mid points of two sides of a triangle, is parallel to the third side and it is equal to one half of its length.

Given: P and Q are midpoints of $\overline{AB}$ and $\overline{AC}$
in $\triangle ABC,$ $\overline{PQ}$ is the line segment joining them.

To Prove: $\overline{PQ}||\overline{BC}$ and $m\overline{PQ}=\frac{1}{2}m\overline{BC}$

Construction: Produce PQ to D such that $\overline{QD}\cong\overline{PQ}$ join D and C.

Proof: