Question

1. for each line segment shown below: (a) use your compass and a straight edge to construct an equilateral triangle whose base is the line segment given and (b) measure each side length to the nearest millimeter. be sure to do the constructions in pencil and leave all construction marks (i.e. the arcs you use to locate the third point).

Explanation:

Step1: Set compass width

Set the compass width to the length of the given line - segment (either AB or CD).

Step2: Draw arcs from endpoints

For a given line - segment (say AB), place the compass at point A and draw an arc. Then place the compass at point B and draw another arc with the same radius. The two arcs will intersect at a point (say C).

Step3: Connect points

Use a straight - edge to connect point A to the intersection point C and point B to the intersection point C. The triangle ABC is an equilateral triangle. Repeat the same process for the other line - segment (CD). To measure the side lengths, use a ruler to measure the distance between the vertices of the constructed equilateral triangles to the nearest millimeter.

Answer:

Follow the above construction steps for each given line - segment to construct equilateral triangles and measure their side lengths with a ruler to the nearest millimeter.