Question

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are \\( \triangle stu \\) and \\( \triangle vwx \\) congruent?

Explanation:

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

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For $ST$: Let $S(- 10,10)$ and $T(-10,0)$, then $ST=\sqrt{(-10+10)^2+(10 - 0)^2}=10$.
For $TU$: Let $T(-10,0)$ and $U(2,10)$, then $TU=\sqrt{(2 + 10)^2+(10-0)^2}=\sqrt{144 + 100}=\sqrt{244}$.
For $SU$: Let $S(-10,10)$ and $U(2,10)$, then $SU=\sqrt{(2 + 10)^2+(10 - 10)^2}=12$.

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

For $VW$: Let $V(-1,-10)$ and $W(6,-10)$, then $VW=\sqrt{(6 + 1)^2+(-10+10)^2}=7$.
For $WX$: Let $W(6,-10)$ and $X(-1,2)$, then $WX=\sqrt{(-1 - 6)^2+(2 + 10)^2}=\sqrt{49+144}=\sqrt{193}$.
For $VX$: Let $V(-1,-10)$ and $X(-1,2)$, then $VX=\sqrt{(-1 + 1)^2+(2 + 10)^2}=12$.

Since the corresponding side lengths of $\triangle STU$ and $\triangle VWX$ are not equal ($ST
eq VW$, $TU
eq WX$), the two triangles are not congruent.

Answer:

No, $\triangle STU$ and $\triangle VWX$ are not congruent.