Question 66
The isosceles triangle $ABC$ has $AB = AC$ and points $M$ and $N$ are taken on $BC$ such that $M$ is between $B$ and $N$. Prove that the following properties are equivalent:
i) $m(\angle MAN) = \frac{1}{2} m(\angle BAC)$;
ii) the segments $[BM]$, $[MN]$ and $[MC]$ are the sides of a triangle in which the opposite angle of $[MN]$ has measure $180^\circ - m(\angle A)$.
i) $m(\angle MAN) = \frac{1}{2} m(\angle BAC)$;
ii) the segments $[BM]$, $[MN]$ and $[MC]$ are the sides of a triangle in which the opposite angle of $[MN]$ has measure $180^\circ - m(\angle A)$.