Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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!!

Sally John Amp Mary Had A Discussion About Quadrilateral PQRS Sally Claimed That The Figure Represents An Isosceles Trapezoid John Claimed That It Is A Nonisosc class=

Sagot :

campip123

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

[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]

[tex]PS=\sqrt{(2-1)^2+(0-4)^2}[/tex]

[tex]PS=[/tex][tex]\sqrt{17}[/tex]

[tex]QR=\sqrt{(13-9)^{2}+(8-10)^{2}}[/tex]

[tex]QR=[/tex][tex]\sqrt{20}[/tex]

Since [tex]PS\neq QR[/tex] (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.

[tex]m=[/tex] [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

SR:  [tex]m=[/tex] [tex]\frac{0-8}{2-13}[/tex]

[tex]m=\frac{8}{11}[/tex]

PQ:  [tex]m=\frac{4-10}{1-9}[/tex]

[tex]m=\frac{6}{8}=\frac{3}{4}[/tex]

since [tex]mSR\neq mPQ[/tex] (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.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.