Question

find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral. answer attempt 2 out of 2 slope of $overline{de}=\frac{6}{8}$ length of $overline{de}=10$ slope of $overline{ef}=\frac{7}{3}$ length of $overline{ef}=sqrt{58}$ slope of $overline{fg}=\frac{6}{8}$ length of $overline{fg}=10$ a square a rectangle a rhombus a parallelogram a generic quadrilateral length of $overline{gd}=sqrt{58}$ st be described as

Explanation:

Step1: Recall properties of quadrilaterals

Parallel - sided quadrilaterals have equal - slope opposite sides.

Step2: Analyze given slopes

Slope of $\overline{DE}=\frac{6}{8}$ and slope of $\overline{FG}=\frac{6}{8}$, so $DE\parallel FG$. Also, slope of $\overline{EF}=\frac{7}{3}$ and slope of $\overline{GD}$ is not given but from side - lengths and other slopes we can analyze the shape.

Step3: Analyze given lengths

Length of $\overline{DE} = 10$, length of $\overline{FG}=10$, length of $\overline{EF}=\sqrt{58}$, length of $\overline{GD}=\sqrt{58}$. Opposite sides are equal in length.

Step4: Determine the quadrilateral type

Since opposite sides are parallel and equal in length, it is a parallelogram. For a square, all sides must be equal and adjacent sides must be perpendicular (product of slopes of adjacent sides is - 1). Here adjacent - side slopes do not give a product of - 1. For a rectangle, adjacent sides must be perpendicular. For a rhombus, all sides must be equal.

Answer:

a parallelogram