Question

is abcd congruent to efgh? justify your answer. yes, because a reflection across the line y = x maps abcd onto efgh. yes, because a translation right 5 units and down 6 units maps abcd onto efgh. no, because ∠c and ∠g do not have the same measure. no, because \\(\overline{ab}\\) and \\(\overline{ef}\\) do not have the same length.

Explanation:

To determine if \(ABCD\) and \(EFGH\) are congruent, we analyze the side lengths. For \(AB\): The coordinates of \(A(-3,0)\) and \(B(-6,2)\). Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(AB=\sqrt{(-6 + 3)^2+(2 - 0)^2}=\sqrt{9 + 4}=\sqrt{13}\). For \(EF\): Coordinates of \(E(0,-3)\) and \(F(3,-6)\). \(EF=\sqrt{(3 - 0)^2+(-6 + 3)^2}=\sqrt{9 + 9}=\sqrt{18}\). Since \(AB\) and \(EF\) have different lengths, the figures can't be congruent.

Answer:

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