Question 178
Consider the triangle $ABC$, with $m(\widehat{A}) \gt 60^\circ$ and $m(\widehat{C}) \gt 30^\circ$. In the half-plane determined by the line $BC$ not containing $A$, consider points $D$ and $E$ so that $m(\widehat{ABE}) = m(\widehat{CBD}) = 90^\circ$ and $m(\widehat{BAE}) = m(\widehat{BCD}) = 60^\circ$. Denote $F$ and $H$ the midpoints of the segments $[AE]$, respectively $[CD]$, and $G$ the common point of the lines $AC$ and $DE$. Show that:
a) $\Delta EBD \sim \Delta ABC$;
b) $\Delta FGH \equiv \Delta ABC$.
a) $\Delta EBD \sim \Delta ABC$;
b) $\Delta FGH \equiv \Delta ABC$.