When constructing an angle bisector, the arcs must intersect in order to divide the angle into two congruent angles. The intersection point of the arcs represents the vertex of the angle, and the radii of the arcs represent the angle's sides. By constructing the arcs to intersect, we ensure that the bisector passes through the vertex and divides the angle into two equal parts. If the arcs did not intersect, the bisector would not be properly constructed and would not bisect the angle correctly.
When constructing an angle bisector, the arcs must intersect in order to ensure the accuracy of the geometric construction. This is because the angle bisector is a line that divides an angle into two equal parts. The arcs are drawn from the vertex of the angle, and they intersect at two points. The angle bisector is then constructed by drawing a line through these two points to divide the angle into two equal parts. If the arcs do not intersect, it would mean that the line connecting the two points does not pass through the vertex of the angle, and therefore it would not accurately divide the angle into two equal parts.
