Problem

Segment \(XY\) is given. Circles centered at \(X\) and \(Y\) with radius \(XY\) meet at \(Z\) and \(W\), and \(Z\) is the specified intersection. Complete the equilateral-triangle construction by stating the radius and centers, intersection used, sides to draw, and resulting side equality.

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radius = XY; centers = X,Y; chosen intersection = Z; side action = draw XZ and YZ; result = XY=XZ=YZ, so XYZ is equilateral

radius = XY; centers = X,Y; chosen point = midpoint XY; side action = join midpoint; result = equilateral

radius = XY; centers = X,Y; chosen intersection = W; side action = connect X-Y-W-Z; result = equilateral

radius = XZ before Z exists; centers = X,Y; chosen point = Z; side action = XZ,YZ; result = equilateral

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