Problem
GEO-B1-M06-P002 The Same Height
#2
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), point \(D\) lies on side \(BC\). Prove that \(S_{ABD}:S_{ACD}=BD:DC\).
Triangles \(ABD\) and \(ACD\) have a common height from \(A\).
Both triangles have the height from point \(A\) to line \(BC\). Therefore their areas are in the ratio of their bases on this line: \(S_{ABD}:S_{ACD}=BD:DC\).
The main pattern for area ratios.