Question

In ΔABC isoscel, [AB]≡[AC], se construiesc inaltimile BD⊥AC, D∈[AC] si CE⊥AB, E∈[AB].
Sa se demonstreze ca ΔBOC este isoscel, unde BD∩CE={O}.
Va rog sa faceti si cu desen, dau coroana si puncte multe cat cuprinde-n contul vostru.

Answer 1

$\it \Delta ABC-isoscel,\ AB=AC \Rightarrow \widehat{ACB}=\widehat{ABC} \Rightarrow \widehat{BCD}=\widehat{CBE}$

$\it Compar\breve am\ \Delta DBC\ cu\ \Delta ECD:\\ \\ \begin{cases}\ sunt\ dreptunghice,\ \widehat{CDB}=\widehat{BEC}=90^o\\ \\ BC\ -\ latur\breve a\ comun\breve a\\ \\ \widehat{BCD}\equiv\ \widehat{CBE}\end{cases}\ \stackrel{IU}{\Longrightarrow} \ \Delta DBC\ \equiv\ \Delta ECD \Rightarrow\\ \\ \\ \Rightarrow\ \widehat{DBC}=\widehat{ECB} \Rightarrow \Delta{BOC}= isoscel$