Question

Daca puteti sa ma ajutati!!!

Answer 1

$\underline{Aratam~ca~triunghiul~DBE~este~isoscel} \\ \\ Deoarece~AD~||~CE~si~AC~||~DE,~rezulta~ca~patrulaterul~ADEC \\ este~paralelogram,~deci~AC=DE,~insa~AC=BD \Rightarrow DE=BD. \\ \\ Astfel~am~demonstrat~ca~ \Delta DBE -isoscel.$
$Rezulta~ca~ \ \textless \ DBC \equiv ~\ \textless \ DEC,~insa~ \ \textless \ DEC \equiv ~ \ \textless \ ACB~(unghiuri~ \\ corespondente) \Rightarrow \ \textless \ DBC \equiv ~\ \textless \ ACB.$

$\underline{Aratam~ca~ \Delta ABC \equiv \Delta DCB } \\ \\ Din~ \ \textless \ ACB \equiv ~\ \textless \ DBC,~ BC=BC,~si~AC=BD \Rightarrow \\ \Delta ABC \equiv \Delta DCB \Longrightarrow \boxed{AB=CD} \Rightarrow \boxed{trapez~isoscel}$