Question

Use a compass and straightedge to construct an equilateral triangle using the length (AB) ̅ for the sides.

Answer 1

For a better understanding of the solution provided here please go through the diagram in the file attached.

Let us begin the construction of the triangle in a step by step fashion.

Step 1 Take AB as the base.

Step 2 Take the point of the compass and place it on A and take the width of the compass to be AB.

Step 3 Make an arc (as shown in green for convenience).

Step 4 Now, take the point of the compass and place it on B keeping the width of the compass to be AB.

Step 5 Make an arc (as shown in yellow for convenience) such that it intersects the arc made in Step 3 at the point C.

Step 6 Join the points A and C, and B and C.

The made triangle is the required equilateral triangle, $\Delta ABC$. All the sides will be equal to the length AB.