Draw a parallelogram ABCD, with AB=6cm, AD=4.8 cm and `angleDAB=45^(@)`.
Draw the perpendicular bisector of side AD and let it meet AD at point P. also, draw the diagonals AC and BD, and let them intersect at point O. join O and P. measure OP. DC=5 cm

Answer

To solve the problem of drawing the parallelogram ABCD with the given dimensions and properties, follow these steps:

### Step-by-Step Solution:

1. **Draw Line Segment AB:**
- Using a ruler, draw a line segment AB that measures 6 cm.
- Label the endpoints as A and B.

**Hint:** Ensure 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 45 degrees. This will be the angle DAB.
- Extend the line from A in the direction of the angle.

**Hint:** Make sure the protractor is aligned correctly with line AB when measuring the angle.

3. **Mark Point D:**
- From point A, measure 4.8 cm along the line you just drew (the direction of angle DAB) and mark this point as D.

**Hint:** Use the compass to measure 4.8 cm accurately if needed.

4. **Draw Line Segment DC:**
- From point D, measure 5 cm in a direction parallel to line AB (to the right) and mark this point as C.

**Hint:** You can use a ruler to ensure that the line is parallel to AB.

5. **Mark Point B:**
- From point B, measure 4 cm downwards (perpendicular to AB) and mark this point as C.

**Hint:** Use a right angle to ensure the line is perpendicular to AB.

6. **Complete the Parallelogram:**
- Connect points C and D to complete the parallelogram ABCD.

**Hint:** Ensure that the opposite sides are equal in length to confirm it is a parallelogram.

7. **Draw the Perpendicular Bisector of AD:**
- To find the midpoint of AD, use a compass to draw arcs above and below the line segment AD from points A and D.
- The intersection points of the arcs will help you draw the perpendicular bisector. Draw a line through these intersection points to find point P.

**Hint:** Make sure the compass is set to more than half the length of AD for accurate arcs.

8. **Draw the Diagonals AC and BD:**
- Draw a line segment from A to C and another from B to D. These are the diagonals of the parallelogram.

**Hint:** Use a ruler to ensure the lines are straight.

9. **Find Intersection Point O:**
- The diagonals AC and BD will intersect at point O. Mark this point.

**Hint:** Ensure that both lines are extended enough to find the intersection clearly.

10. **Join Points O and P:**
- Draw a line segment connecting points O and P.

**Hint:** Use a ruler for a straight line.

11. **Measure OP:**
- Use a ruler to measure the length of segment OP and record the measurement.

**Hint:** Ensure the ruler is aligned properly to get an accurate measurement.

### Final Measurement:
- The length of OP is found to be 3 cm.

### Summary:
You have successfully drawn the parallelogram ABCD, constructed the perpendicular bisector of side AD, drawn the diagonals, and measured the segment OP.