Problem
GEO-B1-M06-P003 Median and Area
#3
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), point \(M\) is the midpoint of side \(BC\). Prove that \(S_{ABM}=S_{ACM}\).
Bases \(BM\) and \(CM\) are equal, and the height from \(A\) is common.
Since \(M\) is the midpoint of \(BC\), \(BM=CM\). Triangles \(ABM\) and \(ACM\) have the common height from \(A\) to line \(BC\). Therefore their areas are equal.
Basic proof of “a median halves area”.