Question

which line segment is a perpendicular bisector? image of a geometric figure with points v, w, u, r, s, t and some right angles and lengths marked as 54

Explanation:

Step1: Recall the definition of a perpendicular bisector

A perpendicular bisector of a segment is a line (or segment) that is perpendicular to the segment (forms a right angle, \(90^\circ\)) and divides the segment into two equal parts (bisects it).

Step2: Analyze the given diagram

• We see that \(VR = VS = 54\) (the lengths from \(V\) to \(R\) and \(V\) to \(S\) are both 54).
• The segment \(VW\) (assuming the right - angled segment at \(W\) on \(RS\)): First, check the right angle (the little square indicates a right angle, so it is perpendicular to \(RS\)). Second, since \(VR = VS = 54\), the point \(W\) (where the right angle is) should be the mid - point of \(RS\) (because in a triangle, if two sides from a common vertex are equal, the perpendicular from that vertex to the base bisects the base). So the segment with the right angle (perpendicular) and bisecting the segment (since \(VR = VS\)) is the one we are looking for. From the diagram, the segment \(VW\) (or the segment with the right angle at \(W\) on \(RS\)) is the perpendicular bisector. But looking at the labels, the segment that is perpendicular (right angle) and bisects (since \(VR = VS\)) is the segment (let's assume the segment is \(VW\) or the one with the right angle on \(RS\)). Wait, more precisely, the segment that is perpendicular to \(RS\) (has the right angle) and since \(VR = VS\), it bisects \(RS\). So the segment with the right angle (perpendicular) and bisecting \(RS\) (because \(VR = VS\)) is the perpendicular bisector. From the diagram, the segment \(VW\) (the one with the right angle at \(W\) on \(RS\)) is the perpendicular bisector. But let's re - check: A perpendicular bisector must be perpendicular (right angle) and bisect (split into two equal parts). Since \(VR = VS = 54\), triangle \(VRS\) is isosceles with \(VR = VS\). The altitude from \(V\) to \(RS\) (the segment with the right angle) will bisect \(RS\) (by the property of isosceles triangles: the altitude, median, and angle bisector from the apex coincide). So the segment with the right angle (perpendicular) and bisecting \(RS\) is the perpendicular bisector. So the segment (let's say \(VW\)) is the perpendicular bisector. But looking at the diagram, the segment with the right angle at \(W\) on \(RS\) (and \(VR = VS = 54\)) is the perpendicular bisector. So the segment is \(VW\) (or the one labeled with the right angle on \(RS\)).

Answer:

The line segment \(VW\) (or the segment with the right angle at \(W\) on \(RS\)) is the perpendicular bisector. (Assuming the labels, the segment with the right angle and bisecting \(RS\) as \(VR = VS\))