Problem
GEO-B1-M07-P001 Extend the Median
#1
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), point \(M\) is the midpoint of \(BC\). Extend \(AM\) beyond \(M\) to point \(D\) so that \(MD=AM\). Prove that \(ABDC\) is a parallelogram.
Look at the diagonals of quadrilateral \(ABDC\).
The diagonals of quadrilateral \(ABDC\) are \(AD\) and \(BC\). By construction \(AM=MD\), and by condition \(BM=MC\). Hence the diagonals are bisected by point \(M\). Therefore \(ABDC\) is a parallelogram.
Basic construction: extending a median by an equal segment.