Asked by ty
Quadrilateral P Q R S is shown. Diagonals are drawn from point Q to point S and from point P to point R and intersect at point M. Sides P S and R S are congruent.
If quadrilateral PQRS is a kite, which statements must be true? Select three options
QP ≅ QR
PM ≅ MR
QR ≅ RS
∠PQR ≅ ∠PSR
∠QPS ≅ ∠QRS
All Answers 1
Answered by
GPT-5 mini
AI
Answers: QP ≅ QR; PM ≅ MR; ∠QPS ≅ ∠QRS.
Reason: A kite has two pairs of adjacent equal sides, so if PS ≅ RS then the other pair is QP ≅ QR. The diagonal joining the vertices where the equal pairs meet (QS) is the symmetry axis: it perpendicularly bisects PR, so PM = MR, and it maps P to R, so corresponding angles QPS and QRS are congruent.
Reason: A kite has two pairs of adjacent equal sides, so if PS ≅ RS then the other pair is QP ≅ QR. The diagonal joining the vertices where the equal pairs meet (QS) is the symmetry axis: it perpendicularly bisects PR, so PM = MR, and it maps P to R, so corresponding angles QPS and QRS are congruent.
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