Question

the figure shows quadrilateral pqrs, diagonals pr and qs intersect at point t. choose all the statements that contain enough information to prove that pqrs is a parallelogram. a. △pqr≅△rsp b. (overline{ps}congoverline{qr}) and (overline{pq}paralleloverline{sr}) c. (angle spqcongangle qrs) and (angle rspcongangle pqr) d. (angle stpcongangle qtr) and (angle ptqcongangle rts)

Explanation:

Step1: Recall parallelogram - criteria

If one - pair of opposite sides is congruent and parallel, or opposite angles are congruent, it's a parallelogram.

Step2: Analyze each option

A: Proves congruent triangles but not parallelogram. B: One - pair congruent and parallel. C: Opposite angles congruent. D: Just angle - equalities for diagonals, not enough.

Answer:

B. $\overline{PS}\cong\overline{QR}$ and $\overline{PQ}\parallel\overline{SR}$
C. $\angle SPQ\cong\angle QRS$ and $\angle RSP\cong\angle PQR$