Question

Carlotta is constructing an equilateral triangle. she has already constructed the line segment and arc shown. what should carlotta do for her next step?

Answer 1

Carlotta should draw two equal arcs using a compass set to the length of her line segment, place the compass at both ends of the segment, draw the arcs, and use the intersection point to create the third vertex of the equilateral triangle.

Step-by-step explanation:

To construct an equilateral triangle, Carlotta has completed the first step by drawing a line segment. The next step in the construction is to create two equal arcs with the same radius as the length of the line segment. To do this, she should:

1. Place the compass at one end of the line segment and draw an arc above the line.
2. Without changing the compass width, place the compass at the other end of the line segment and draw another arc that intersects the first arc.
3. The point where the two arcs intersect gives the third vertex of the equilateral triangle.
4. Finally, draw line segments from this new point to the ends of the original line segment to complete the triangle.

Using this method, the length of the sides of the triangle will be equal, ensuring the triangle is equilateral.