Problem
GEO-B1-M06-P007 Equal Areas on a Common Base
#7
★★☆☆☆ Level 2 of 5
Triangles \(ABC\) and \(ABD\) have common base \(AB\). Prove that if \(CD\parallel AB\), then \(S_{ABC}=S_{ABD}\).
The distances from \(C\) and \(D\) to line \(AB\) are equal.
Since \(CD\parallel AB\), points \(C\) and \(D\) lie on one line parallel to base \(AB\). Therefore the heights to base \(AB\) are equal. The base is common, so the areas are equal.
A standard problem on equal heights between parallel lines.