Using ruler and compasses only, construct a parallelogram ABCD, in which : `AB=6cm,AD=3cm and angleDAB=60^(@)`.
In the same figure draw the bisector of angle DAB and let it meet DC at point P. measure angle APB.

Answer

### Step-by-Step Construction of Parallelogram ABCD

1. **Draw Line Segment AB**:
- Using a ruler, draw a line segment AB of length 6 cm.

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

2. **Construct Angle DAB**:
- At point A, use a protractor to measure and draw an angle of 60° with line AB. Label the ray as AD.

**Hint**: Remember to mark the angle clearly to avoid confusion later.

3. **Measure Length AD**:
- From point A along ray AD, measure and mark a point D such that AD = 3 cm.

**Hint**: Use the ruler to measure 3 cm accurately from point A along the ray AD.

4. **Draw Arc from Point D**:
- With the compass, set the width to 6 cm (the length of AB) and place the compass point on D. Draw an arc above the line.

**Hint**: Make sure the arc is drawn clearly so that it can intersect with the next arc.

5. **Draw Arc from Point B**:
- Now, set the compass width to 3 cm (the length of AD) and place the compass point on B. Draw an arc that intersects the previous arc.

**Hint**: Ensure you draw the arc wide enough to see where it intersects the first arc.

6. **Label the Intersection Point as C**:
- Mark the point where the two arcs intersect as point C.

**Hint**: Use a pencil to mark the intersection clearly, as this point is crucial for the next steps.

7. **Draw Line Segments BC and CD**:
- Use the ruler to draw line segments BC and CD to complete the parallelogram ABCD.

**Hint**: Ensure that lines are straight and connect the points accurately.

8. **Bisect Angle DAB**:
- To bisect angle DAB, place the compass point at A and draw an arc that intersects both rays AD and AB. Label the intersection points as E and F.

**Hint**: Make sure the arc is not too small; it should clearly intersect both lines.

9. **Draw the Bisector**:
- Using the ruler, draw a line from A through the intersection point of the arcs drawn from points E and F. Extend this line until it intersects line DC at point P.

**Hint**: Ensure that the line is straight and extends far enough to intersect line DC.

10. **Measure Angle APB**:
- Use a protractor to measure the angle APB.

**Hint**: Align the protractor accurately to ensure a correct measurement.

### Final Note:
After completing these steps, you will have constructed the required parallelogram ABCD and the angle bisector of angle DAB, along with the measurement of angle APB.