Question

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are \\( \triangle qrs \\) and \\( \triangle abc \\) congruent?

Explanation:

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

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(AB\): \(A(- 10,-4)\), \(B(0,-4)\), \(AB=\sqrt{(0 + 10)^2+(-4+4)^2}=\sqrt{100}=10\).
For \(BC\): \(B(0,-4)\), \(C(-10,8)\), \(BC=\sqrt{(-10 - 0)^2+(8 + 4)^2}=\sqrt{100 + 144}=\sqrt{244}\).
For \(AC\): \(A(-10,-4)\), \(C(-10,8)\), \(AC=\sqrt{(-10+10)^2+(8 + 4)^2}=\sqrt{144}=12\).

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

For \(QR\): \(Q(10,4)\), \(R(1,4)\), \(QR=\sqrt{(10 - 1)^2+(4 - 4)^2}=\sqrt{81}=9
eq10\).

Since \(AB
eq QR\), the two triangles do not have all corresponding sides equal.

Answer:

No, \(\triangle QRS\) and \(\triangle ABC\) are not congruent.