Question

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are \\( \triangle efg \\) and \\( \triangle uvw \\) congruent?

Explanation:

Step1: Check side - lengths using distance formula

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(\triangle EFG\):
Let \(E(0,10)\), \(F(- 8,1)\), \(G(-8,10)\)
\(EF=\sqrt{(0 + 8)^2+(10 - 1)^2}=\sqrt{64 + 81}=\sqrt{145}\)
\(FG=\sqrt{(-8+8)^2+(10 - 1)^2}=9\)
\(EG=\sqrt{(0 + 8)^2+(10 - 10)^2}=8\)

For \(\triangle UVW\):
Let \(U(-2,-10)\), \(V(-10,-2)\), \(W(-2,-2)\)
\(UV=\sqrt{(-2 + 10)^2+(-10 + 2)^2}=\sqrt{64+64}=\sqrt{128}\)
\(VW=\sqrt{(-2 + 10)^2+(-2 + 2)^2}=8\)
\(UW=\sqrt{(-2+2)^2+(-10 + 2)^2}=8\)

Since the side - lengths of \(\triangle EFG\) and \(\triangle UVW\) are not equal.

Answer:

No, \(\triangle EFG\) and \(\triangle UVW\) are not congruent.