Two adjacent sides of a parallelogram are 4 cm and 6 cm respectively. The angle between them is `60^(@)`. Construct the parallelogram.

Answer

To construct a parallelogram with adjacent sides of lengths 4 cm and 6 cm, and an angle of 60 degrees between them, follow these steps:

### Step-by-Step Solution:

1. **Draw Line Segment AB**:
- Start by drawing a horizontal line segment AB that measures 4 cm.
- Use a ruler to ensure the length is accurate.

**Hint**: Make sure to label the endpoints clearly as A and B.

2. **Construct Angle at Point B**:
- At point B, use a protractor to measure an angle of 60 degrees from line AB.
- Mark this angle with a light pencil line extending from point B.

**Hint**: Ensure that the protractor is aligned correctly with line AB to get an accurate angle.

3. **Draw Line Segment BC**:
- From point B, draw a line along the 60-degree angle you just marked.
- Measure 6 cm along this line and mark the endpoint as C.

**Hint**: Use the ruler to measure exactly 6 cm from point B to point C.

4. **Draw Line Segment AC**:
- Now, draw a line segment from point A to point C. This line will not be parallel to AB but will help in finding the next point.

**Hint**: This line will help you visualize where point D will be located.

5. **Construct Angle at Point A**:
- At point A, you need to construct an angle of 120 degrees (since the angles in a parallelogram are supplementary).
- Use the protractor to measure 120 degrees from line AC and mark this angle.

**Hint**: Remember that 120 degrees is the same as 180 degrees - 60 degrees.

6. **Draw Line Segment AD**:
- From point A, draw a line along the 120-degree angle you just marked.
- Measure 6 cm along this line and mark the endpoint as D.

**Hint**: Ensure that the line AD is equal in length to BC, which is 6 cm.

7. **Complete the Parallelogram**:
- Finally, connect points C and D with a straight line to complete the parallelogram ABCD.

**Hint**: Ensure that the opposite sides AB and CD are equal, and AD and BC are equal in length.

### Final Check:
- Measure all sides to confirm that AB = CD = 4 cm and BC = AD = 6 cm.
- Check the angles to ensure that angle ABC = 60 degrees and angle DAB = 120 degrees.