Construct a kite ABCD in which AB=4cm, AD=6cm and AC=6cm.

Answer

To construct a kite ABCD with the given dimensions AB = 4 cm, AD = 6 cm, and AC = 6 cm, follow these steps:

### Step-by-Step Solution:

1. **Draw the Diagonal AC**:
- Use a ruler to draw a horizontal line segment AC measuring 6 cm. Label the endpoints as A and C.
- **Hint**: Ensure that you measure accurately using the ruler for the length of AC.

2. **Construct Point B**:
- Place the compass point at A and set the compass width to 4 cm (the length of AB).
- Draw an arc above the line AC. This arc represents all possible locations for point B.
- **Hint**: Make sure the compass is not too loose, so the arc remains a perfect circle.

3. **Construct Point D**:
- Now, place the compass point at C and set the compass width to 6 cm (the length of AC).
- Draw another arc above the line AC. This arc represents all possible locations for point D.
- **Hint**: Keep the compass point steady while drawing the arc to ensure accuracy.

4. **Locate Points B and D**:
- The intersection of the two arcs you drew from A and C will give you the points B and D. Label these intersection points as B and D.
- **Hint**: If the arcs intersect at two points, choose one point for B and the other for D.

5. **Connect the Points**:
- Use a ruler to connect points A to B, B to C, C to D, and D to A.
- **Hint**: Ensure that the lines are straight and connect the points accurately.

6. **Verify the Dimensions**:
- Measure the lengths AB, AD, and AC to confirm they are 4 cm, 6 cm, and 6 cm respectively.
- **Hint**: Use the ruler to double-check each length to ensure the kite is constructed correctly.

### Final Result:
You should now have a kite ABCD with the specified dimensions. The kite will have two pairs of equal adjacent sides, confirming its properties.