Question

in the given figure angle Bed equal to Angle B D E and e is the midpoint of BC prove that AF/CF=AD/BE

Answer 1

Answer:

given  ∠ BED=∠BDE

E is mid point  of BC

prove AF/CF=AD/BE

Step-by-step explanation:

through draw C  CG||FD

proof  in Δ AFD,CG||FD

,AC/AF=AG/GD....(1)

  +1 both sides

AC/FC+1=AG/GD+1

AC+AC/FC=AG+GD/GD

therefore AF/Cf=AD/GD....(2)

in Δ BCG ,DE||GC

BE/EC=BD/GD

since BE=EC( E is mid point of BC

therefore  BD=GD....(3)

  since  ∵BD=BE  ....(4)

in ∠BED=∠BDE

substituting  3 in 1

BE/EC=BD/GD....5)

substituting 4 in 5

AF/CF=AD/BE    hence proved

hope its helped

Answer 2

Answer:

given  ∠ BED=∠BDE

E is mid point  of BC

prove AF/CF=AD/BE

Step-by-step explanation:

through draw C  CG||FD

proof  in Δ AFD,CG||FD

,AC/AF=AG/GD....(1)

 +1 both sides

AC/FC+1=AG/GD+1

AC+AC/FC=AG+GD/GD

therefore AF/Cf=AD/GD....(2)

in Δ BCG ,DE||GC

BE/EC=BD/GD

since BE=EC( E is mid point of BC

therefore  BD=GD....(3)

 since  ∵BD=BE  ....(4)

in ∠BED=∠BDE

substituting  3 in 1

BE/EC=BD/GD....5)

substituting 4 in 5

AF/CF=AD/BE    hence proved

hope its helped