Construct a regular pentagon within a circle of diameter 70mm?

To construct a regular pentagon within a circle of diameter 70mm, follow these steps:

1. Draw a circle with a diameter of 70mm. This will be the circumcircle of the pentagon.

2. Draw a horizontal line through the center of the circle. This will be the base of the pentagon.

3. Use a protractor to divide the circle into 5 equal parts, each measuring 72 degrees. These points will be the vertices of the pentagon.

4. Connect the points to form the sides of the pentagon.

5. The length of each side of the pentagon will be equal to the radius of the circle, which is half of the diameter (35mm).

6. Check that all angles are equal and that the sides are of equal length to ensure that the pentagon is regular.

Materials:

- Compass
- Ruler
- Pencil

Steps:

1. Draw the circle: Use the compass to draw a circle with a diameter of 70mm.

2. Mark the center of the circle: Using the ruler, draw a vertical and horizontal line through the center of the circle to form two perpendicular diameters.

3. Divide the circle into 5 equal parts: To do this, mark a point on the circle at the intersection of the horizontal diameter and the circle. Then, use the compass to measure and mark off four equal distances along the circle.

4. Connect the points: Use the ruler to connect the five points marked on the circle. This will form the pentagon.

Additional Tips:

- To ensure accuracy, make sure the points are evenly spaced around the circle.
- Use a sharp pencil and a steady hand for precise lines.
- If the measurements are slightly off, adjust the points accordingly until the pentagon fits perfectly within the circle.