Question

the graph shows triangles jkl and qrs. is jkl congruent to qrs? justify your answer. yes, because a reflection across the x - axis maps jkl onto qrs. yes, because a rotation 90° clockwise around the origin maps jkl onto qrs. no, because ∠j and ∠q do not have the same measure. no, because (overline{jk}) and (overline{qr}) do not have the same length.

Explanation:

Step1: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(JK\), if \(J(- 2,-4)\) and \(K(-7,-2)\), then \(JK=\sqrt{(-7 + 2)^2+(-2 + 4)^2}=\sqrt{25 + 4}=\sqrt{29}\).
For \(QR\), if \(Q(-3,3)\) and \(R(-2,7)\), then \(QR=\sqrt{(-2+3)^2+(7 - 3)^2}=\sqrt{1 + 16}=\sqrt{17}\).

Step2: Check congruence condition

Since \(JK
eq QR\), triangles \(JKL\) and \(QRS\) are not congruent.

Answer:

No, because \(\overline{JK}\) and \(\overline{QR}\) do not have the same length.