When constructing an angle bisector, the arcs must intersect because the bisector divides the angle into two equal parts, and the arc on each side represents the distance covered by those equal parts, ensuring the angle is divided accurately.
When constructing an angle bisector, the arcs must intersect because the angle bisector divides the angle into two equal parts, and the arcs serve as a visual representation of those equal parts. If the arcs do not intersect, it would imply that the division of the angle is not equal, violating the purpose of constructing an angle bisector.
When constructing an angle bisector, the arcs must intersect because the two arcs are segments of circles centered at the vertex of the angle, and the angle bisector is defined by the line passing through the vertex and intersecting both arcs, dividing the angle into two equal halves.
