Problem
GEO-B1-M07-P014 Find a Midpoint Through a Parallel
#14
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(D\) is the midpoint of \(AB\). Through \(D\), a line parallel to \(AC\) meets \(BC\) at point \(E\). Prove that \(E\) is the midpoint of \(BC\).
Compare \(\triangle BDE\) and \(\triangle BAC\).
Since \(DE\parallel AC\), triangles \(BDE\) and \(BAC\) are similar. From \(BD:BA=1:2\), it follows that \(BE:BC=1:2\). Hence \(BE=EC\), so \(E\) is the midpoint of \(BC\).
A version of the same tool in another orientation.