Given:
PQRS is a rhombus.
PO = 4 cm, OQ = 3 cm.

To Find:
Value of PR and SQ.

Solution:

Step 1: Understanding the properties of a rhombus:
- A rhombus is a quadrilateral with all sides of equal length.
- The diagonals of a rhombus bisect each other at right angles.

Step 2: Drawing a diagram:
- Draw a rhombus PQRS.
- Mark the given measurements: PO = 4 cm and OQ = 3 cm.
- Draw the diagonals PO and QS that intersect at point O.

Step 3: Analyzing the diagram:
- Since PQRS is a rhombus, all sides are equal in length.
- Therefore, PR = PQ = QR = RS.
- The diagonals PO and QS bisect each other at right angles.
- Thus, triangle POS and triangle QOR are congruent by the side-angle-side (SAS) congruence theorem.

Step 4: Applying the congruence theorem:
- We know that triangle POS and triangle QOR are congruent.
- Therefore, corresponding sides of these triangles are equal.
- So, PS = SR and OR = OP.

Step 5: Calculating the value of PR:
- PR = PS + SR (by the property of a rhombus)
- PR = PQ + QR (since PS = PQ and SR = QR)
- PR = PQ + PS (since PS = SR)
- PR = 2PQ (since PQ = QR = PR/2)

Step 6: Calculating the value of PR:
- PR = 2PQ
- PR = 2(OP + OQ) (substituting the values of PQ and QR)
- PR = 2(4 + 3) (substituting the given values of OP and OQ)
- PR = 2(7)
- PR = 14 cm

Step 7: Calculating the value of SQ:
- Since PR = QR = RS (by the property of a rhombus)
- SQ = PR + QR (by the property of a rhombus)
- SQ = PR + PR (since QR = PR)
- SQ = 2PR
- SQ = 2(14)
- SQ = 28 cm

Step 8: Conclusion:
- The value of PR is 14 cm and SQ is 28 cm.

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