Construction of Quadrilateral PQRS

To construct a quadrilateral PQRS, we need to follow the given measurements and ensure that the sides and angles are consistent with the given information.

Step 1: Draw a line segment PQ of length 3cm.
- Take a ruler and draw a line segment PQ of length 3cm. Label the endpoints as P and Q.

Step 2: From point P, draw a line segment PR of length 8cm.
- Using a ruler, draw a line segment PR of length 8cm starting from point P. Label the endpoint as R.

Step 3: From point Q, draw a line segment QS of length 4cm.
- Use a ruler to draw a line segment QS of length 4cm starting from point Q. Label the endpoint as S.

Step 4: From point R, draw a line segment RS of length 3cm.
- Using a ruler, draw a line segment RS of length 3cm starting from point R. Label the endpoint as S.

Step 5: From point S, draw a line segment SP of length 7.5cm.
- Use a ruler to draw a line segment SP of length 7.5cm starting from point S. Label the endpoint as P.

Step 6: Verify the measurements and angles.
- Measure the lengths of all the sides using a ruler to ensure they match the given measurements.
- Check the angles to make sure they are consistent with the given information.

Justification:

We can justify the construction of quadrilateral PQRS by checking the measurements and angles.

- PQ = 3cm (Given)
- RS = 3cm (Given)
- PS = 7.5cm (Given)
- PR = 8cm (Given)
- SQ = 4cm (Given)

The lengths of all the sides match the given measurements, confirming the accuracy of the construction.

To further verify the construction, we can check the angles of the quadrilateral:

- Angle PQR
- Angle PQS
- Angle PSR
- Angle SRQ

Using a protractor, measure these angles and compare them to the given information. If the angles match, it confirms the construction of quadrilateral PQRS.

In conclusion, by following the given measurements and verifying the lengths of the sides and angles, we have successfully constructed quadrilateral PQRS.