if quadrilateral pqrs is a kite, which statements must be true? select three options\n□qp≅qr\n□pm≅mr\n□qr≅rs\…

if quadrilateral pqrs is a kite, which statements must be true? select three options\n□qp≅qr\n□pm≅mr\n□qr≅rs\n□∠pqr≅∠psr\n□∠qps≅∠qrs

if quadrilateral pqrs is a kite, which statements must be true? select three options\n□qp≅qr\n□pm≅mr\n□qr≅rs\n□∠pqr≅∠psr\n□∠qps≅∠qrs

Answer

Explanation:

Step1: Recall kite - properties

A kite has two pairs of adjacent congruent sides. In kite (PQRS), (\overline{QP}\cong\overline{QR}) and (\overline{SP}\cong\overline{SR}). Also, the diagonals of a kite are perpendicular, and the diagonal that connects the vertices of the non - congruent angles bisects the other diagonal. So (\overline{PM}\cong\overline{MR}). And the angles between the non - congruent sides are congruent, i.e., (\angle PQR\cong\angle PSR).

Step2: Analyze each option

  • (\overline{QP}\cong\overline{QR}): True by the definition of a kite (two pairs of adjacent congruent sides).
  • (\overline{PM}\cong\overline{MR}): True because the diagonal (QS) bisects the diagonal (PR).
  • (\overline{QR}\cong\overline{RS}): False. In a kite, we have (\overline{QP}\cong\overline{QR}) and (\overline{SP}\cong\overline{SR}), not (\overline{QR}\cong\overline{RS}).
  • (\angle PQR\cong\angle PSR): True as the angles between the non - congruent sides of a kite are congruent.
  • (\angle QPS\cong\angle QRS): False. There is no such property for a kite.

Answer:

(\overline{QP}\cong\overline{QR}), (\overline{PM}\cong\overline{MR}), (\angle PQR\cong\angle PSR)