Question

In a figure,triangle ABC is an isosceles triangle in which AB=AC. If E and F be the midpoints of AC and AB respectively ,prove that BE=CF.
please give the solution now is urgent

Answer 1

see, AB = AC
and E is the mid point on AB,
⇒ AE = BE
⇒AB = AE + BE 
         =AE + AE = 2AE
⇒AB = 2AE
and F is the mid point of AC
⇒AF = CF
AC= AF + CF
     =CF + CF
     =2CF 
AC= 2 CF
∵ AB = AC
∴ 2 AE = 2 CF
⇒ AE = CF    (proved )

Answer 2

In triangle BFC and EBC,
BF=CE
Angle B = Angle C
BC=BC 
Triangle BFC is congruent to Triangle ECB by SAS test
Therefore, BE=CF (By cpct)