Question

if quadrilateral pqrs is a kite, which statements must be true? select three options.
□qp≅qr
□pm≅mr
□qr≅rs
□∠pqr≅∠psr
□∠qps≅∠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 is bisected by the other.

Step2: Analyze side - equalities

In kite \(PQRS\), \(\overline{QP}\cong\overline{QR}\) and \(\overline{SP}\cong\overline{SR}\) because of the definition of a kite (two pairs of adjacent - equal sides). Also, the diagonal \(\overline{PR}\) is bisected by the other diagonal \(\overline{QS}\), so \(\overline{PM}\cong\overline{MR}\).

Step3: Analyze angle - equalities

The non - vertex angles of a kite are equal. The vertex angles are not equal in general. So, \(\angle PQR\cong\angle PSR\).

Answer:

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