Question 103
A regular triangular pyramid $SABC$ has vertex $S$ and the planes $\alpha, \beta$ are such that $BC \subset \alpha, \alpha \perp (SAB), AB \subset \beta$ and $\beta \perp (SBC)$.
a) Show that if $\angle(\alpha, \beta) = 120^\circ$, then $SABC$ is a regular tetrahedron.
b) If $H$ is the orthocentre of the tetrahedron $SABC$ and $\angle AHC = 90^\circ$, then $\angle ASB = \angle ASC = \angle BSC = 90^\circ$.
a) Show that if $\angle(\alpha, \beta) = 120^\circ$, then $SABC$ is a regular tetrahedron.
b) If $H$ is the orthocentre of the tetrahedron $SABC$ and $\angle AHC = 90^\circ$, then $\angle ASB = \angle ASC = \angle BSC = 90^\circ$.