Giải thích các bước giải:
Ta có:
$\left\{ \begin{array}{l}
{V_{S.ANC}} = \dfrac{1}{3}.{S_{SAN}}.d(C,(SAN))\\
{V_{S.AMN}} = \dfrac{1}{3}.{S_{SAN}}.d(M,(SAN))\\
d(M,(SAN)) = \dfrac{1}{2}d(C,(SAN))
\end{array} \right. \Rightarrow {V_{S.AMN}} = \dfrac{1}{2}{V_{S.ANC}}(1)$
Và:
$\begin{array}{l}
{V_{S.ANC}} = \dfrac{1}{3}.{S_{ANC}}.d(S,(ANC)) = \dfrac{1}{3}.\dfrac{1}{4}{S_{ABC{\rm{D}}}}.d({\rm{S}},(ABC{\rm{D}}))\\
= \dfrac{1}{4}.\left( {\dfrac{1}{3}{S_{ABC{\rm{D}}}}.d({\rm{S}},(ABC{\rm{D}}))} \right) = \dfrac{1}{4}.{V_{S.ABC{\rm{D}}}}
\end{array}(2)$
Từ (1),(2) suy ra: ${V_{S.AMN}} = \dfrac{1}{2}{V_{S.ANC}} = \dfrac{1}{8}.{V_{S.ABC{\rm{D}}}}$(Đpcm)
