Problem
GEO-B1-M06-P015 Three Equal Parts of the Base
#15
★★★☆☆ Level 3 of 5
On side \(BC\) of triangle \(ABC\), points \(D\) and \(E\) are marked so that \(BD=DE=EC\). Prove that \(S_{ABD}=S_{ADE}=S_{AEC}\).
All three triangles have the height from \(A\) to line \(BC\).
Triangles \(ABD\), \(ADE\), \(AEC\) have bases \(BD\), \(DE\), \(EC\) on one line \(BC\) and a common height from \(A\). Since the bases are equal, the areas are equal.
A simple but important model of splitting area by the base.