Constructing an Equilateral Triangle with Perimeter 19.5 cm

To construct an equilateral triangle with a perimeter of 19.5 cm, we need to ensure that all three sides are equal in length. Since the perimeter is given as 19.5 cm, each side of the equilateral triangle will be 6.5 cm (since 19.5 cm ÷ 3 sides = 6.5 cm).

Measuring the Angles of the Equilateral Triangle

To verify that each angle of the equilateral triangle measures 60°, we can use the fact that the sum of the interior angles of a triangle is always 180°. Since all three angles of an equilateral triangle are equal, each angle will be 60°.

Explanation

- Construct a line segment of 6.5 cm using a ruler.
- Using a compass, draw arcs on both ends of the line segment to create two points that are 6.5 cm apart.
- Connect the endpoints of the line segment to the new points to form an equilateral triangle.
- Measure the angles of the triangle using a protractor. Each angle should measure 60°.
- To further verify, you can check that the sum of the three angles is 180°.

By following these steps and measurements, you can construct an equilateral triangle with a perimeter of 19.5 cm and verify that each angle measures 60°.