Construct a trapezium PQRs in which `PQ||SR,PQ=6.5cm, QR=4.5cm, PS=6cm` and `/_Q=60^(@)`.

Answer

To construct the trapezium PQRS with the given conditions, follow these steps:

### Step-by-Step Construction:

1. **Draw the Base PQ:**
- Draw a line segment PQ measuring 6.5 cm.
- Label the endpoints as P and Q.

**Hint:** Use a ruler to measure and draw the line accurately.

2. **Construct Angle Q:**
- At point Q, use a protractor to construct an angle of 60 degrees.
- Draw a ray QR making a 60-degree angle with line PQ.

**Hint:** Ensure the protractor is aligned correctly with line PQ to measure the angle accurately.

3. **Mark Point R:**
- From point Q, measure 4.5 cm along the ray QR and mark this point as R.

**Hint:** Use a compass or ruler to ensure the distance is exactly 4.5 cm.

4. **Construct Angle R:**
- Now, at point R, we need to construct an angle of 120 degrees (since angle Q + angle R = 180 degrees).
- Use the protractor to measure 120 degrees from line QR and draw a ray RS.

**Hint:** Remember that 120 degrees is measured counter-clockwise from the line QR.

5. **Mark Point S:**
- From point R, measure 6 cm along the ray RS and mark this point as S.

**Hint:** Again, ensure that the distance is measured accurately.

6. **Complete the Trapezium:**
- Finally, connect points P and S with a straight line to complete the trapezium PQRS.

**Hint:** Use a ruler to draw the line PS straight and ensure it connects properly with points P and S.

### Final Check:
- Ensure that PQ is parallel to SR.
- Verify the lengths: PQ = 6.5 cm, QR = 4.5 cm, PS = 6 cm, and angle Q = 60 degrees.