Question

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are \\( \triangle t u v \\) and \\( \triangle q r s \\) congruent?

Explanation:

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

• Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
• \(TV=\sqrt{(9 - 1)^2+(0 - 8)^2}=\sqrt{64 + 64}=\sqrt{128}\)
• \(UV=\sqrt{(10 - 1)^2+(9 - 8)^2}=\sqrt{81+1}=\sqrt{82}\)
• \(TU = 9\)

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

• \(QR=\sqrt{(1 - (- 10))^2+(0 - (-1))^2}=\sqrt{121 + 1}=\sqrt{122}\)
• \(RS=\sqrt{(-7-(-10))^2+(-8 - (-1))^2}=\sqrt{9 + 49}=\sqrt{58}\)
• \(QS=\sqrt{(1-(-7))^2+(0 - (-8))^2}=\sqrt{64 + 64}=\sqrt{128}\)

Step3: Compare the side lengths

• Since the side lengths of \(\triangle TUV\) and \(\triangle QRS\) are not all equal.

Answer:

\(\triangle TUV\) and \(\triangle QRS\) are not congruent.