Question

(from unit 1, lesson 5.) 5. this diagram is a straightedge and compass construction. which triangle is equilateral? explain how you know.

Explanation:

Step1: Recall equilateral - triangle property

An equilateral triangle has all sides equal. In a straight - edge and compass construction, equal - length segments are created by the compass.

Step2: Analyze the construction

The circles are drawn with the same radius. If we consider the segments formed by the intersection points of the circles, for example, if we take a triangle formed by the centers of three circles that intersect each other and have the same radius, the lengths of the sides of the triangle are equal to the radius of the circles. Let's assume the centers of the circles are the vertices of the triangle. Since all the circles have the same radius, the distances between the centers of the circles (sides of the triangle) are equal.

Answer:

The triangle formed by the centers of the circles (for example, if the centers are labeled as points, the triangle with vertices at those points) is equilateral because the sides of the triangle are equal to the radius of the congruent circles used in the construction.