Question

the graph shows quadrilaterals defg and pqrs. is defg congruent to pqrs? justify your answer. yes, because a rotation 90° counterclockwise around the origin maps defg onto pqrs. yes, because a reflection across the y - axis maps defg onto pqrs. no, because \\( \overline{gd} \\) and \\( \overline{sp} \\) do not have the same length. no, because \\( \angle d \\) and \\( \angle p \\) do not have the same measure.

Explanation:

Step1: Calculate the length of \(GD\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(G(4,4)\) and \(D(2,6)\), \(GD=\sqrt{(4 - 2)^2+(4 - 6)^2}=\sqrt{4 + 4}=\sqrt{8} = 2\sqrt{2}\).

Step2: Calculate the length of \(SP\)

For \(S(-4,4)\) and \(P(-5,2)\), \(SP=\sqrt{(-4+ 5)^2+(4 - 2)^2}=\sqrt{1+4}=\sqrt{5}\).
Since \(GD
eq SP\), the quadrilaterals are not congruent.

Answer:

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