VTMO 2026 - Grade 7 - Final - SET 3 - Self-study Question 5

In triangle $ABC$, let $M$ be the midpoint of $BC$ and $N$ the midpoint of $AM$. On the ray opposite to ray $NB$, choose $D$ so that $DN=NB$. Let $E$ be the intersection of rays $CD$ and $BA$.

a) Prove that $CD=AM$.

b) Prove that $AB=AE$.