Construct a parallelogram ABCD in which diagonal AC=3.8 cm, diagonal BD=4.6cm and the angle between AC and BD is `60^(@)`.

Answer

To construct a parallelogram ABCD with diagonals AC = 3.8 cm, BD = 4.6 cm, and the angle between them being 60 degrees, follow these steps:

### Step-by-Step Solution:

1. **Draw Diagonal AC**:
- Using a ruler, draw a line segment AC measuring 3.8 cm. Label the endpoints as A and C.

**Hint**: Ensure that you measure accurately using the ruler for precise construction.

2. **Find the Midpoint O of AC**:
- To find the midpoint O of AC, measure 1.9 cm from point A towards C (which is half of 3.8 cm) and mark this point as O.

**Hint**: You can use a compass to measure 1.9 cm from point A to find the midpoint accurately.

3. **Draw an Angle of 60 Degrees**:
- At point O, use a protractor to measure an angle of 60 degrees. Mark this angle by drawing a ray OB upwards.

**Hint**: Make sure the protractor is aligned properly with line AC to get an accurate angle measurement.

4. **Draw Diagonal BD**:
- From point O, measure 2.3 cm along the ray OB (which is half of diagonal BD = 4.6 cm) and mark this point as D.

**Hint**: Use a compass to measure 2.3 cm accurately from point O to point D.

5. **Draw an Arc from Point D**:
- With the compass set to 2.3 cm, place the compass point on D and draw an arc above and below the line OB. This will help locate point B.

**Hint**: Ensure that the compass remains at the same width while drawing the arc.

6. **Draw an Arc from Point C**:
- Now, with the compass still set to 2.3 cm, place the compass point on C and draw another arc that intersects the previous arcs drawn from point D.

**Hint**: The intersection points of the arcs will help you find point B.

7. **Label Point B**:
- Mark the intersection point of the arcs as point B.

**Hint**: You may have two intersection points; choose the one that makes sense in the context of the parallelogram.

8. **Connect the Points**:
- Finally, connect the points A to B, B to D, D to C, and C to A to complete the parallelogram ABCD.

**Hint**: Use a ruler to ensure that all lines are straight and accurately drawn.

### Final Construction:
You should now have a parallelogram ABCD with the specified dimensions and angle.