Question
4. Construct a trapezium PQRS having PQ = 10cm QR = 4cm RS = 6cm and SP = 3cm with PQ // SR
Answers
GPT-4o mini
To construct trapezium PQRS with the given dimensions and properties, follow these steps:
1. **Draw the Base:** Start by drawing the longer base PQ, which measures 10 cm.
2. **Setup the Parallel Line:** Since PQ is parallel to SR (PQ || SR), you will need to draw a second line that will represent the shorter base SR. Use a ruler to ensure this line is parallel to PQ and will eventually measure 6 cm.
3. **Locate Points Q and P:**
- Mark point P at one end of the line PQ and point Q at the other end.
- Label PQ as 10 cm.
4. **Draw the Side QR:**
- From Point Q, use a compass to measure 4 cm directly upwards (or downwards, based on your construction preference) to locate point R.
- Mark point R.
5. **Draw the Side SP:**
- From point P, also use a compass to measure 3 cm directly upwards (or downwards) to locate point S.
- Mark point S.
6. **Draw the Shorter Base SR:**
- Measure the distance between points R and S. You want this length to be 6 cm. Adjust the position of point S or R to ensure that the distance between them is exactly 6 cm.
- Draw line segment SR.
7. **Final Check:**
- Ensure that PQ is parallel to SR and that the lengths of QR and SP are correct.
By following these steps, you should have constructed trapezium PQRS with the sides PQ = 10 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm with PQ parallel to SR.
Make sure to double-check all measurements to ensure accuracy.
1. **Draw the Base:** Start by drawing the longer base PQ, which measures 10 cm.
2. **Setup the Parallel Line:** Since PQ is parallel to SR (PQ || SR), you will need to draw a second line that will represent the shorter base SR. Use a ruler to ensure this line is parallel to PQ and will eventually measure 6 cm.
3. **Locate Points Q and P:**
- Mark point P at one end of the line PQ and point Q at the other end.
- Label PQ as 10 cm.
4. **Draw the Side QR:**
- From Point Q, use a compass to measure 4 cm directly upwards (or downwards, based on your construction preference) to locate point R.
- Mark point R.
5. **Draw the Side SP:**
- From point P, also use a compass to measure 3 cm directly upwards (or downwards) to locate point S.
- Mark point S.
6. **Draw the Shorter Base SR:**
- Measure the distance between points R and S. You want this length to be 6 cm. Adjust the position of point S or R to ensure that the distance between them is exactly 6 cm.
- Draw line segment SR.
7. **Final Check:**
- Ensure that PQ is parallel to SR and that the lengths of QR and SP are correct.
By following these steps, you should have constructed trapezium PQRS with the sides PQ = 10 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm with PQ parallel to SR.
Make sure to double-check all measurements to ensure accuracy.