Answer :
In a rhombus, the following geometric properties are always true:
Statement A: PR is perpendicular to QS.
- This is true. In a rhombus, the diagonals (PR and QS) are always perpendicular to each other. They bisect each other at right angles (90°).
Statement B: PQR is supplementary to QPS.
- This is true. In a rhombus, consecutive angles are supplementary to each other. Since PQR and QPS are consecutive angles, they add up to 180°.
Statement C: PS is parallel to QR.
- This is true. In a rhombus, opposite sides are always parallel. Therefore, PS is parallel to QR.
Statement D: ZQPS is supplementary to QRS.
- This statement is false. The notation here is incorrect and ambiguous; ZQPS is not a standard geometric notation. The intended meaning seems to be that QP and QR angles should add up to 180°, but this would only be correct if we were discussing consecutive angles in the context properly defined.
Statement E: PR & QS
- This statement is incomplete and without a clear context. It provides no meaningful information about the geometric properties.
Statement F: PQ = RS
- This is true. In a rhombus, all sides are equal. Thus, PQ is equal to RS.
Based on these explanations, the statements that are true are A, B, C, and F.
Statement A: PR is perpendicular to QS.
- This is true. In a rhombus, the diagonals (PR and QS) are always perpendicular to each other. They bisect each other at right angles (90°).
Statement B: PQR is supplementary to QPS.
- This is true. In a rhombus, consecutive angles are supplementary to each other. Since PQR and QPS are consecutive angles, they add up to 180°.
Statement C: PS is parallel to QR.
- This is true. In a rhombus, opposite sides are always parallel. Therefore, PS is parallel to QR.
Statement D: ZQPS is supplementary to QRS.
- This statement is false. The notation here is incorrect and ambiguous; ZQPS is not a standard geometric notation. The intended meaning seems to be that QP and QR angles should add up to 180°, but this would only be correct if we were discussing consecutive angles in the context properly defined.
Statement E: PR & QS
- This statement is incomplete and without a clear context. It provides no meaningful information about the geometric properties.
Statement F: PQ = RS
- This is true. In a rhombus, all sides are equal. Thus, PQ is equal to RS.
Based on these explanations, the statements that are true are A, B, C, and F.
