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