Question

select the correct answer. a quadrilateral has vertices a(3, 5), b(2, 0), c(7, 0), and d(8, 5). which statement about the quadrilateral is true? a. abcd is a parallelogram with non - perpendicular adjacent sides. b. abcd is a trapezoid with only one pair of parallel sides. c. abcd is a rectangle with non - congruent adjacent sides. d. abcd is a rhombus with non - perpendicular adjacent sides.

Explanation:

Step1: Calculate the slopes of the sides

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Slope of $AB$ with $A(3,5)$ and $B(2,0)$: $m_{AB}=\frac{0 - 5}{2 - 3}=\frac{- 5}{-1}=5$.
Slope of $BC$ with $B(2,0)$ and $C(7,0)$: $m_{BC}=\frac{0 - 0}{7 - 2}=0$.
Slope of $CD$ with $C(7,0)$ and $D(8,5)$: $m_{CD}=\frac{5 - 0}{8 - 7}=5$.
Slope of $DA$ with $D(8,5)$ and $A(3,5)$: $m_{DA}=\frac{5 - 5}{3 - 8}=0$.
Since $m_{AB}=m_{CD}$ and $m_{BC}=m_{DA}$, $AB\parallel CD$ and $BC\parallel DA$, so $ABCD$ is a parallelogram.

Step2: Check for perpendicular - adjacent sides

The product of the slopes of two perpendicular lines is $- 1$.
$m_{AB}\times m_{BC}=5\times0 = 0
eq - 1$, so adjacent sides are not perpendicular.

Answer:

A. $ABCD$ is a parallelogram with non - perpendicular adjacent sides.