Question

Put the steps in order for constructing an equilateral triangle, given segment ab as the side length.

1) Draw segment ab
2) Construct a circle with center a and radius ab
3) Construct a circle with center b and radius ab
4) The equilateral triangle cannot be constructed with the given information

Answer 1

To construct an equilateral triangle using segment AB as the side, draw segment AB, construct two circles centered at A and B with radius AB, and mark the point of intersection as the third vertex to form the triangle.

Step-by-step explanation:

To construct an equilateral triangle given segment AB as the side length, we could follow the following steps:

1. Draw segment AB, which will be one side of our equilateral triangle.
2. Construct a circle with center A and radius AB. This will give us all the points that are at the same distance from A as B is, one of which will be another vertex of our triangle.
3. Construct a circle with center B and radius AB. Similarly, this provides all the points equidistant from B, and its intersection with the first circle gives us the third vertex of the triangle.
4. Where the two circles intersect, mark a point C. This point is equidistant from A and B, and AB is equidistant from A and C, thus creating an equilateral triangle.

By following these steps, we have used the defining property of an equilateral triangle—that all sides are of equal length—to accurately construct such a triangle with the given segment AB as one side.