In the diagram, $AD = DC$, $AE = EB$, and the lines $BD$ and $CE$ of $\Delta ABC$ intersec

Question

In the diagram, $AD = DC$, $AE = EB$, and the lines $BD$ and $CE$ of $\Delta ABC$ intersect at $G$. The points $F$ and $H$ are the midpoints of $BG$ and $CG$ respectively. Prove that $DEFH$ is a parallelogram, $BF = DG$ and $CH = GE$.

Accepted Answer

(a) Proved: $DEFH$ is a parallelogram (b) Proved: $BF=DG$ and $CH=GE$

Proofs in Plane Geometry - Midpoint Theorem

Proofs in Plane Geometry - Midpoint Theorem

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