Question

use the information in the given figure to prove AB is equal to FE BD is equal to CF

Answer 1

ab is || to fe, therefore angle efd = angle abc
angle c is already = d therefore angle e is also equal to a,
by this we can prove that both triangles are similar 
the ratio of sides are equal when triangles are similar , i.e ac/de = ba/fe=bc/df
we know that ac = de , therefore all sides are equal as well 
so , ab = fe (i)
now we know that bc = df and dc is a common segment to both lines , therefore 
bc = df
bc -dc = df - dc 
bd = cf