A trapezoid is a quadrilateral with two unequal parallel sides and two lateral sides.
Looking at the quadrilateral ABCD in the graph
The slope of BC is equal to that of AD and they are parallel to each other, HENCE, ABCD SATISFY THE CONDITION OF A TRAPEZOID
Also, for the side AB and CD, if they have the same slope and distance they are isosceles.
so we will have to check using the formula
[tex]\text{slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]
A(2,2) and B (3,5)
The slope of AB =
[tex]\text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{5\text{ -2}}{3-2}\text{ =}\frac{3}{1}\text{ = 3}[/tex]
C (6,5) and D (8,2)
The slope of CD =
[tex]\text{slope = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{2\text{ -5}}{8\text{ -6}}\text{ =}\frac{-3}{-2}\text{ =}\frac{3}{2}[/tex]
We can also find the distance between AB and CD
A(2,2) and B (3,5)
[tex]\text{distance AB =}\sqrt[]{(5-2)^2+(3-2)^2}\text{ = }\sqrt[]{3^2\text{ +1}}\text{ =}\sqrt[]{10}[/tex]
C (6,5) and D (8,2)
[tex]\begin{gathered} \text{distance CD =}\sqrt[]{(2-5)^2+(8-6)^2}\text{ =}\sqrt[]{-3^2+2^2\text{ }}=\text{ }\sqrt[]{13} \\ \end{gathered}[/tex]
Since distance, AB is not equal to CD, and the slopes of the two lines are
different. Then ABCD is not Isosceles Trapezoid.
