In triangle ABC, D and E are the mid-points of AB and AC (see the tick marks). The blue segment DE is 6.5 cm long. Find BC.

**Theorem (Mid-Point)**: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.

In ΔABC, let D be midpoint of AB and E be midpoint of AC. Then DE ∥ BC and DE = (1/2) × BC.

**Converse**: A line through the midpoint of one side parallel to another side will bisect the third.

In ΔABC, if D is midpoint of AB and a line through D parallel to BC meets AC at E, then E is the midpoint of AC.

**Use**: this theorem solves a huge class of problems where you have midpoints of triangle sides — you can immediately conclude parallelism and half-length.