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Step-by-step explanation:
BF * CE = BE * DF
Step-by-step explanation:
ABCD is a square the bisector of angle DBC cut AC and CD at E and F respectively prove that BF into CE is equal to BE into DF
ABCD is a square
=> AC & BD makes 45° Angled with Sides
the bisector of angle DBC = ∠DBF = ∠CBF = 45/2 = 22.5°
∠CBE = ∠CBF = 22.5°
in ΔBDF & ΔBCE
∠DBF = ∠CBE = 22.5°
∠BDF = ∠BDC = 45° & ∠BCA = ∠BCE = 45°
=> ∠BDF = ∠BCE
if two angles are equal then third angle also would be equal
=> ΔBDF ≅ ΔBCE
=> DF/CE = BF/BE
=> DE * BE = BF * CE
=> BF * CE = BE * DF
QED
Proved
not my own answer.... hope it helps
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