Question

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are △uvw and △fgh congruent?

Explanation:

Step1: Calculate the side lengths of \(\triangle UVW\)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(UV\): \(U(-9,7)\), \(V(-9,-1)\), \(d_{UV}=\sqrt{(-9+9)^2+(7 + 1)^2}=8\)
For \(VW\): \(V(-9,-1)\), \(W(0,7)\), \(d_{VW}=\sqrt{(0 + 9)^2+(7+1)^2}=\sqrt{81 + 64}=\sqrt{145}\)
For \(UW\): \(U(-9,7)\), \(W(0,7)\), \(d_{UW}=\sqrt{(0 + 9)^2+(7 - 7)^2}=9\)

Step2: Calculate the side lengths of \(\triangle FGH\)

For \(FG\): \(F(8,-1)\), \(G(-3,-1)\), \(d_{FG}=\sqrt{(8 + 3)^2+(-1+1)^2}=11\)
Since \(11
eq8\), \(11
eq9\), \(11
eq\sqrt{145}\)

Answer:

\(\triangle UVW\) and \(\triangle FGH\) are not congruent.