Question

the perpendicular bisector of a segment
is a set of two sectors
that are next to each
other.
cuts the segment in
half, intersecting the
segment at a 90-
degree angle,
cuts the segment into
thirds at a 90-degree
angle.
cuts the segment in half
and can cross the
segment at any angle.

Explanation:

Step1: Recall the definition of perpendicular bisector

A perpendicular bisector of a segment cuts the segment into two equal parts (bisects it) and is perpendicular (intersects at a \(90^{\circ}\) angle) to the segment.

Step2: Analyze each option

• Green option: A perpendicular bisector is not a set of two sectors next to each other.
• Blue option: Cuts the segment in half (bisects) and intersects at a \(90 -\) degree angle. This matches the definition.
• Orange option: Cuts into thirds is wrong, it should cut into halves.
• Cyan option: Must intersect at \(90^{\circ}\), not any angle.

Answer:

The blue - colored option (cuts the segment in half, intersecting the segment at a 90 - degree angle) is correct.