Question

ABCD is a square the bisector of angle DBC cut AC and CD at E and F respectively prove that b f into C is equal to p into DF

Answer 1

Answer:

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

Answer 2

Answer:

Step-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