Problem
GEO-B1-M06-P004 Vertices on a Parallel Line
#4
★☆☆☆☆ Level 1 of 5
Points \(C\) and \(D\) lie on a line parallel to \(AB\). Prove that \(S_{ABC}=S_{ABD}\).
The triangles have common base \(AB\) and equal heights.
Triangles \(ABC\) and \(ABD\) have common base \(AB\). The heights from \(C\) and \(D\) to \(AB\) are equal because these points lie on a line parallel to \(AB\). Hence the areas are equal.
Checks understanding of height as the distance between parallel lines.