classify the quadrilateral shown on the graph. rectangle trapezoid square rhombus

Explanation:

Step1: Recall properties of quadrilaterals

A rectangle has four right - angles, a square is a rectangle with all sides equal, a trapezoid has one pair of parallel sides, and a rhombus has all sides equal.

Step2: Check side - length and angle properties

Let the vertices of the quadrilateral be (A(- 5,0)), (B(0,4)), (C(5,0)), (D(0,-4)). The distance between two points ((x_1,y_1)) and ((x_2,y_2)) is given by (d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}). For (AB=\sqrt{(0 + 5)^2+(4 - 0)^2}=\sqrt{25 + 16}=\sqrt{41}). (BC=\sqrt{(5 - 0)^2+(0 - 4)^2}=\sqrt{25 + 16}=\sqrt{41}). (CD=\sqrt{(0 - 5)^2+(-4 - 0)^2}=\sqrt{25 + 16}=\sqrt{41}). (DA=\sqrt{(-5 - 0)^2+(0 + 4)^2}=\sqrt{25 + 16}=\sqrt{41}). So all sides are equal. The slope of (AB) is (m_{AB}=\frac{4-0}{0 + 5}=\frac{4}{5}), the slope of (BC) is (m_{BC}=\frac{0 - 4}{5 - 0}=-\frac{4}{5}), (m_{AB}\times m_{BC}\neq - 1), so the angles are not right - angles. Since all sides are equal and the angles are not right - angles, it is a rhombus.

Answer:

Rhombus