Tinem cont ca in orice triunghi suma unghiurilor este de 180°.
[tex]\measuredangle EBD=90^\circ\implies \measuredangle BED+\measuredangle BDE=90^\circ\implies \measuredangle BED=90^\circ-\measuredangle BDE\\\\dar \ \measuredangle BDE=\measuredangle D=\cfrac{\measuredangle A}{2}\\\\[/tex]
[tex]\\\implies\boxed{ \measuredangle BED=90^\circ-\cfrac{\measuredangle A}{2}}\\\\pe \ de\ alta\ parte, \\\measuredangle ABC=\measuredangle ACB\\[/tex]
[tex]\measuredangle ABC+\measuredangle ACB+\measuredangle BAC=180^\circ\\\\\implies 2\measuredangle ABC+\measuredangle BAC=180^\circ\\\\\implies 2\measuredangle ABC+ \measuredangle A=180^\circ\ \Big| :2\\\\\implies \measuredangle ABC+\cfrac{\measuredangle A}{2}=90^\circ\\\\\implies \boxed{\measuredangle ABC=90^\circ-\cfrac{\measuredangle A}{2}}[/tex]
[tex]deci \ \boxed{\measuredangle BED=\measuredangle ABC}[/tex]
Aceste doua unghiuri sunt alterne interne, considerant dreptele BC si ED impreuna cu secanta EB, iar fiindca sunt egale inseamna ca BC e paralela cu ED.
