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In quadrilateral $PQRS$, sides $\overline {PS}$ and $\overline {QR}$ have equal length and sides $\overline{PQ}$ and $\overline{RS}$ are parallel to each other. Point $X$ is the intersection of the diagonals $\overline {PR}$ and $\overline {QS}.$ Which of the following conclusions must be true?

A) $\triangle PXQ\cong\triangle RXS$

B) $\triangle SPR\cong\triangle RQS$

C) $\triangle SPQ\cong\triangle QRS$

Type your answer as a list of letters separated by commas. For instance, if you believe that conditions A, B, and C are enough, then type "A,B,C" into the answer box. If you believe none of the options are correct, enter "none."

 Sep 14, 2019
 #1
avatar+103858 
+1

I think the following image is what we need

 

 

This figure is an isosceles trapezoid....PQ is parallel to RS  and PS = QR

And the diagonals of an isosceles trapezoid are equal

And SR = SR

And PS = QR

 

Therefore...by SSS....triangle SPR is congruent to triangle RQS →   "B"

 

 

cool cool cool

 Sep 14, 2019
edited by CPhill  Sep 14, 2019
edited by CPhill  Sep 14, 2019

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