Problem
GEO-B1-M08-P007 Extending a Median
#7
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(M\) is the midpoint of \(BC\). Extend \(AM\) beyond \(M\) to \(D\), where \(MD=AM\). Prove that \(AB\parallel CD\) and \(AC\parallel BD\).
You can prove a parallelogram or two pairs of congruent triangles.
Point \(M\) is the midpoint of \(BC\) and, by construction, the midpoint of \(AD\). Hence the diagonals of quadrilateral \(ABDC\) are bisected by point \(M\). Therefore \(ABDC\) is a parallelogram, so \(AB\parallel CD\) and \(AC\parallel BD\).
Checks whether the student remembers the auxiliary construction from the toolbox module.