Question

construct an equilateral triangle (not inscribed in a circle). use the drawing tool to complete the construction.

Explanation:

Step1: Draw a line segment

Draw a line segment, say \( AB \), of any length. This will be one side of the equilateral triangle.

Step2: Construct 60° angles

Using a compass and straightedge (or the drawing tool's line and angle features), construct a 60° angle at point \( A \) and at point \( B \). The rays of these angles will intersect at a point, say \( C \).

Step3: Form the triangle

The triangle \( ABC \) formed by the segments \( AB \), \( AC \), and \( BC \) is an equilateral triangle because all sides are equal (since the angles are 60°, by the properties of triangles, the sides opposite equal angles are equal, and with two 60° angles at \( A \) and \( B \), the third angle at \( C \) is also 60°, making all sides equal).

Answer:

An equilateral triangle is constructed with side \( AB \), and vertices \( A \), \( B \), \( C \) where \( \angle A=\angle B = \angle C=60^{\circ} \) and \( AB = BC=AC \). (The actual drawing would show the three connected line segments with equal length and 60° angles between them.)