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