Answer :
Final answer:
Statements B, C, D, and F are true for a rhombus, where the diagonals are perpendicular, opposite angles are supplementary, and opposite sides are parallel. The other options provided are not valid statements regarding the properties of a rhombus.
Explanation:
If PQRS is a rhombus, certain properties must inherently be true. A rhombus is a special type of parallelogram where all four sides are of equal length. Reflecting on the principles of affine geometry, it can be examined which of the statements provided in the question must be true.
- B. PR is perpendicular to QS: This is true for a rhombus because the diagonals of a rhombus bisect each other at right angles.
- C. PQR is supplementary to QPS: This statement must be true since opposite angles in any parallelogram, including a rhombus, are supplementary.
- D. PS is parallel to QR: This is true as the opposite sides of a rhombus are parallel to each other.
- F. QPS is supplementary to Z QRS: This statement holds since adjacent angles in a parallelogram (and by extension, a rhombus) are supplementary.
It is important to note that the letters alone like 'A. PRQS' or 'E. PQRS' are incomplete or irrelevant statements regarding the properties of the rhombus and thus are not considered true or valid statements.
