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

Question

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

Uniteasy Admin · Accepted Answer

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 
$$ 	herefore CF = BG $$
 $$ \because  BE=CF $$
$$ 	herefore BE = BG $$
$$	herefore  DE=DF $$

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