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. Also, the diagonals of a kite are perpendicular, and one diagonal is bisected by the other.

Step2: Analyze side - equalities

In kite \(PQRS\), the adjacent sides are equal. So, \(\overline{QP}=\overline{QR}\) and \(\overline{SP}=\overline{SR}\). Also, the diagonal \(\overline{PR}\) is bisected by the diagonal \(\overline{QS}\), so \(\overline{PM}=\overline{MR}\).

Step3: Analyze angle - equalities

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

Answer:

1. \(\overline{QP}=\overline{QR}\)
2. \(\overline{PM}=\overline{MR}\)
3. \(\angle PQR=\angle PSR\)