Problem
GEO-B1-M07-P002 Parallel Through a Midpoint
#2
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), point \(D\) is the midpoint of \(AB\). Through \(D\), a line parallel to \(BC\) meets \(AC\) at point \(E\). Prove that \(E\) is the midpoint of \(AC\).
Use the similarity \(\triangle ADE\sim\triangle ABC\).
Since \(DE\parallel BC\), triangles \(ADE\) and \(ABC\) are similar. Since \(D\) is the midpoint of \(AB\), \(AD:AB=1:2\). Hence \(AE:AC=1:2\), so \(AE=EC\). Therefore \(E\) is the midpoint of \(AC\).
Main example of drawing a parallel line inside a triangle.