a quadrilateral has vertices a(4, 9), b(2, 5), c(8, 2), and d(10, 6). 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 noncongruent adjacent sides.d. abcd is a square.e. abcd is a rhombus with non-perpendicular adjacent sides.

Option C is correct.

Step-by-step explanation:

Given a quadrilateral has vertices A(4, 9), B(2, 5), C(8, 2), and D(10, 6). we have to check the statements which are true.

Using distance formula,

Opposite sides of quadrilateral are equal.

Now, we have to find the slope of sides to find the angle between the sides of quadrilateral.

Adjacent sides has the slopes negative reciprocals.

⇒ Adjacent sides of the quadrilateral are perpendicular.

hence,  ABCD is a rectangle with non-congruent adjacent sides.

Option C is correct.