Isosceles and equilateral triangles

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Now Playing:Isosceles and equilateral triangles – Example 1a

Find x.
In $\triangle DEF$ , $\overline {EY}$ is a perpendicular line to $\overline {DF}$ and $Y$ is the midpoint of $\overline {DF}$ . Why is $\triangle DEF$ an isosceles triangle? Show your reasoning.

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