Question

from unit 1, lesson 4
here is a straightedge and compass construction.
use a straightedge to draw an equilateral triangle on the figure.
explain how you know the triangle is equilateral.

Explanation:

Step1: Connect the marked points

Use a straightedge to connect three of the marked intersection points of the circles.

Step2: Use circle properties

Since all the circles have the same radius (as they are constructed with a compass), the lengths of the sides of the triangle (which are chords of these congruent circles) are equal. In a triangle, if all three sides are equal, by the definition of an equilateral triangle, the triangle is equilateral.

Answer:

Connect three of the marked intersection points. The triangle is equilateral because all sides are equal (as the circles have the same radius, so the distances between the intersection points are equal).