Question

ABCD este patrat, E∈(DC), F∈(DA, astfel incat AF=CE si A este intre D si F. Determinati m(unghiului BDE)

Answer 1

Comparam ΔBEC cu ΔBAF
<ECB=<FAB=90
AF=CE (din ipoteza)
AB=BC
=>ΔBEC = ΔBAF
=> BF=BE
=> ΔBFE=isoscel
=> <BFE=<BEF

in ΔDFE avem: <DEF=90-<DFE=90-<AFE
in ΔFAB avem: <AFB=<AFE+<EFB
dar <BEC=<AFB si <EFB=<FEB
=>  <BEC=<FEB+<AFE
Si avem
<DEF+      <FEB+ <BEC=180
(90-<AFE)+<FEB+(<FEB+<AFE)=180
=> 90-2*FEb=180
=> <FEB=90/2=45°
=> <EFB=<FEB=45