is $ \triangle efg $ an isosceles triangle? justify your answer.
yes, $ overline{ef} $ is congruent to $ overline{fg} $.
yes, $ overline{ef} $ is congruent to $ overline{eg} $.
yes, $ overline{eg} $ is congruent to $ overline{fg} $.
no, no two sides are congruent.

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Accepted Answer

# Explanation:
## Step1: Use the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For points $E(-2,2)$, $F(7,-1)$:
$$
\begin{align*}
EF&=\sqrt{(7 + 2)^2+(-1 - 2)^2}\
&=\sqrt{81 + 9}\
&=\sqrt{90}
\end{align*}
$$
For points $E(-2,2)$, $G(-2,-7)$:
$$
\begin{align*}
EG&=\sqrt{(-2+ 2)^2+(-7 - 2)^2}\
&=\sqrt{0+81}\
&=9
\end{align*}
$$
For points $F(7,-1)$, $G(-2,-7)$:
$$
\begin{align*}
FG&=\sqrt{(-2 - 7)^2+(-7+1)^2}\
&=\sqrt{81 + 36}\
&=\sqrt{117}
\end{align*}
$$
# Answer:
No, no two sides are congruent.

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Explanation:

Step1: Use the distance formula

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