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In quadrilateral PQRS, sides PS and QR have equal length and sides PQ and rs are parallel to each other. Point X is the intersection of the diagonals PR and 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 9, 2023
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Since PS = QR and PQ || RS, quadrilateral PQRS is a parallelogram. Therefore, diagonals PR and QS bisect each other at X, so PXQ = RXS and SPR = RQS. Also, SPQ = QRS. So, all the conclusions must be true. The answer is

A,B,C.

 Sep 9, 2023

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