Problem
GEO-B1-M08-P012 Point on a Median
#12
★★★☆☆ Level 3 of 5
In triangle \(ABC\), median \(AM\) is drawn to \(BC\). Point \(P\) lies on \(AM\). Prove that \(S_{PAB}=S_{PAC}\).
Line \(AP\) passes through the midpoint of \(BC\).
Since \(P\) lies on median \(AM\), line \(AP\) passes through the midpoint of \(BC\). Triangles \(PAB\) and \(PAC\) have common base \(AP\), and points \(B\) and \(C\) are equally distant from line \(AP\). Therefore the areas are equal.
Checks whether the student chooses areas instead of angles.