Question

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are \\( \triangle rst \\) and \\( \triangle cde \\) congruent?

Explanation:

Step1: Find the side lengths of \(\triangle RST\)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(RS\): \(R(1,-3)\), \(S(-10,-3)\)
\(RS=\sqrt{(1 - (-10))^2+(-3-(-3))^2}=\sqrt{(11)^2+0^2}=11\)
For \(ST\): \(S(-10,-3)\), \(T(-5,2)\)
\(ST=\sqrt{(-5 - (-10))^2+(2-(-3))^2}=\sqrt{(5)^2+(5)^2}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}\)
For \(RT\): \(R(1,-3)\), \(T(-5,2)\)
\(RT=\sqrt{(-5 - 1)^2+(2-(-3))^2}=\sqrt{(-6)^2+(5)^2}=\sqrt{36+25}=\sqrt{61}\)

Step2: Find the side lengths of \(\triangle CDE\)

For \(CD\): \(C(0,9)\), \(D(10,9)\)
\(CD=\sqrt{(10 - 0)^2+(9 - 9)^2}=\sqrt{(10)^2+0^2}=10\)
Since \(RS = 11
eq CD = 10\)

Answer:

No, \(\triangle RST\) and \(\triangle CDE\) are not congruent.