It is true that the quadrilateral EFGH is a trapezoid but not an isosceles trapezoid
The coordinates are given as:
- E = (-3,-5)
- F = (-2,0)
- G = (2,3)
- H = (5,1)
How to prove that EFGH is not an trapezoid
Start by calculating the slopes of the parallel sides (i.e. sides FG and EH) using the following slope formula
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{FG} = \frac{3-0}{2 +2}[/tex]
[tex]m_{FG} = \frac{3}{4}[/tex]
[tex]m_{EH} = \frac{1 +5}{5 +3}[/tex]
[tex]m_{EH} = \frac{6}{8}[/tex]
Reduce the fraction
[tex]m_{EH} = \frac{3}{4}[/tex]
By comparison, the slopes of the parallel sides are equal (i.e 3/4)
Next, calculate the side lengths of the slant sides (i.e. EF and GH) using the following distance formula
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]d_{EF} = \sqrt{(-2 +3)^2+ (0+5)^2 }[/tex]
[tex]d_{EF} = \sqrt{26}[/tex]
[tex]d_{GH} = \sqrt{(5 -2)^2 + (1 - 3)^2}[/tex]
[tex]d_{GH} = \sqrt{13}[/tex]
By comparison, the side lengths of the slant sides are not equal
Because the slant sides do not have congruent side lengths, and the slopes of the parallel sides are equal; then the quadrilateral EFGH is a trapezoid but not an isosceles trapezoid
Read more about isosceles trapezoids at:
https://brainly.com/question/4758162
