[tex]\it BA\perp(AA'D)\ \ \ \ (1)\\ \\ AO\perp A'D\ \ \ \ \ (2)\\ \\ AO,\ A'D\subset (AA'D)\ \ \ \ (3)\\ \\ (1),\ (2),\ (3)\ \stackrel{T3\perp}{\Longrightarrow}\ BO\perp A'D\ \ \ \ (4)\\ \\ O\in A'D \Rightarrow A'D=OD\ \ \ \ (5)\\ \\ (4),\ (5)\Rightarrow BO\perp OD[/tex]