Question

classify quadrilateral efgh.
(1 point)
rectangle
trapezoid
parallelogram
rhombus

Explanation:

Step1: Recall the definitions

• Rectangle: A parallelogram with four right - angles.
• Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
• Trapezoid: A quadrilateral with exactly one pair of parallel sides.
• Rhombus: A parallelogram with all sides equal.

Step2: Analyze the slopes of the sides

Let \(E(- 4,7)\), \(F(2,7)\), \(G(2,-2)\), \(H(-4,0)\)
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Slope of \(EF\): \(m_{EF}=\frac{7 - 7}{2-(-4)}=\frac{0}{6}=0\)
Slope of \(FG\): \(m_{FG}=\frac{-2 - 7}{2 - 2}\), since \(x_2=x_1 = 2\), \(FG\) is a vertical line (undefined slope)
Slope of \(GH\): \(m_{GH}=\frac{0-(-2)}{-4 - 2}=\frac{2}{-6}=-\frac{1}{3}\)
Slope of \(HE\): \(m_{HE}=\frac{7 - 0}{-4-(-4)}=\frac{7}{0}\), since \(x_2=x_1=-4\), \(HE\) is a vertical line (undefined slope)

Since \(EF\) and \(GH\) are not parallel (\(m_{EF} = 0\) and \(m_{GH}=-\frac{1}{3}\)), and \(FG\) and \(HE\) are parallel (both vertical lines). A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Answer:

Trapezoid