These statements are true:
\(\bold{First.} \ \overline{PS} \ is \ parallel \ to \ \overline{QR}\)
This is true because of the definition of a rhombus which states that opposite sides are parallel.
\(Then \ \overline{PS} \ is \ opposite \ to \ \overline{QR}\)
\(\bold{Second.} \ \overline{PR} \ is \ perpendicular \ to \ \overline{QS}\)
This is true because the diagonals of a rhombus bisect each other at right angles.
\(\bold{Third.} \ \overline{PQ}=\overline{RS}\)
This is true because the four sides of a rhombus are all equals.
\(\bold{Fourth.} \ \angle PQR \ is \ supplementary \ to \ \angle QPS\)
This is also true. Two angles are supplementary when they add up to 180 degrees. Angles in rhombus are equal two to two. Let's name:
\(\angle PQR = \alpha \ and \ \angle QPS = \beta\)
Then it is true that:
\(\angle PQR=\angle PSR \ and \ \angle QPS=\angle QRS\)
Besides, a rhombus is a quadrilateral and it is true that the interior angles of a quadrilateral add up to 360 degrees, thus:
\(2\alpha+2\beta=360 \\ \\ \therefore \boxed{\alpha+\beta = 180^\circ}\)
