A Midpoint Segment Parallel to an Angle Bisector

Problem

In triangle $ABC$ shown, $AD$ is the bisector of angle $A$ , with $D$ on $BC$ , and $AB<AC$ . Point $E$ lies on segment $AC$ with $CE=AB$ . Let $M$ and $N$ be the midpoints of $BC$ and $AE$ respectively.

Prove that $MN\parallel AD$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Triangle Geometry

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