Question

1. which statement about an equilateral triangle constructed using compass and straightedge is always true? (1) each angle measures 90° (2) all three sides are radii of congruent circles (3) the triangle must be inscribed in a circle (4) the triangle has exactly one line of symmetry

Explanation:

• Option 1: Angles in equilateral triangle are \(60^\circ\), not \(90^\circ\) (right angle). Eliminate.
• Option 2: When constructing with compass/straightedge, sides are radii of congruent circles (since compass sets equal radii). This holds.
• Option 3: Not all equilateral triangles are inscribed in a circle (though they can be, but "must" is false). Eliminate.
• Option 4: Equilateral triangle has 3 lines of symmetry, not 1. Eliminate.

Answer:

(2) All three sides are radii of congruent circles