Question

if quadrilateral pqrs is a kite, which statements must be true? select three options.
□(overline{qp}=overline{qr})
□(overline{pm}=overline{mr})
□(overline{qr}=overline{rs})
□(angle pqr=angle psr)
□(angle qps=angle qrs)

Explanation:

Step1: Recall kite - properties

A kite has two pairs of adjacent sides that are equal. The diagonals of a kite are perpendicular, and one diagonal bisects the other diagonal.

Step2: Analyze side - length statements

In a kite \(PQRS\), we have \(\overline{QP}=\overline{QR}\) (adjacent - side property) and \(\overline{PM}=\overline{MR}\) (diagonal - bisecting property).

Step3: Analyze angle - measure statements

The non - vertex angles between the non - equal sides are equal, i.e., \(\angle PQR=\angle PSR\).

Answer:

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