Question

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are △ghi and △def congruent?

Explanation:

Step1: Calculate the side lengths of $\triangle DEF$

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For $DE$: $D(-7,2)$, $E(-3,-3)$
$$DE=\sqrt{(-3 + 7)^2+(-3 - 2)^2}=\sqrt{16 + 25}=\sqrt{41}$$
For $EF$: $E(-3,-3)$, $F(2,2)$
$$EF=\sqrt{(2 + 3)^2+(2 + 3)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}$$
For $DF$: $D(-7,2)$, $F(2,2)$
$$DF=\sqrt{(2 + 7)^2+(2 - 2)^2}=\sqrt{81}=9$$

Step2: Calculate the side lengths of $\triangle GHI$

For $GH$: $G(8,-9)$, $H(3,-3)$
$$GH=\sqrt{(3 - 8)^2+(-3 + 9)^2}=\sqrt{25 + 36}=\sqrt{61}$$
For $HI$: $H(3,-3)$, $I(-1,-9)$
$$HI=\sqrt{(-1 - 3)^2+(-9 + 3)^2}=\sqrt{16 + 36}=\sqrt{52}$$
For $GI$: $G(8,-9)$, $I(-1,-9)$
$$GI=\sqrt{(-1 - 8)^2+(-9 + 9)^2}=\sqrt{81}=9$$

Step3: Compare the side lengths

Since the side lengths of $\triangle DEF$ ($\sqrt{41},5\sqrt{2},9$) and $\triangle GHI$ ($\sqrt{61},\sqrt{52},9$) are not all equal.

Answer:

No, $\triangle GHI$ and $\triangle DEF$ are not congruent.