In the triangle △ ABC , AB=AC , E is a point on AB , F is on extension line of AC , BE=CF , prove DE=DF 。

Draw a parallel line to BC through point F . The line intersects AB at point G .

\because BD \parallel GF

△ABC and △AGF are similar triangles.

\because △ABC is isoscles triangle

\therefore CF = BG

\because BE=CF

\therefore BE = BG

\therefore DE=DF