Question

Sally, John & Mary had a discussion about Quadrilateral PQRS. Sally claimed that the figure represents an isosceles trapezoid, John claimed that it is a non-isosceles trapezoid, while Mary said it wasn’t a trapezoid at all.
Explain how you would prove who is correct.



Prove who is correct. Must show all work!!

Answer 1

Answer:

Step-by-step explanation:

Find the lenghth of the left and right sides using the distance formula to determine if the trapeziod is isosceles

$d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}$

$PS=\sqrt{(2-1)^2+(0-4)^2}$

$PS=$$\sqrt{17}$

$QR=\sqrt{(13-9)^{2}+(8-10)^{2}}$

$QR=$$\sqrt{20}$

Since $PS\neq QR$ (the sides are not equal) this is not an isosceles trapezoid

Sally is incorrect and John is possibly correct.

Find the slope of the top and bottom sides to determine if this is a trapezoid.

$m=$ $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

SR:  $m=$ $\frac{0-8}{2-13}$

$m=\frac{8}{11}$

PQ:  $m=\frac{4-10}{1-9}$

$m=\frac{6}{8}=\frac{3}{4}$

since $mSR\neq mPQ$ (the slopes are not equal) the top and bottom sides are not parallel therefore this is not a trapezoid. Hence, John is incorrect, and Mary is ultimately correct.