Question

arun followed the following instructions.

• draw an angle using a straightedge with vertex point (q). place points (p) and (r) at the end of the non - collinear segments (overline{qp}) and (overline{qr}).
• using a compass, draw an arc that intersects both sides of the angle. place two points, (a) and (b), at the intersection of the arc with both sides of the angle.
• placing the pointed end of the compass on point (a), draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.
• placing the pointed end of the compass on point (b), draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.
• place point (c) at the intersection of the two smaller arcs and draw a segment from the vertex point (q) to point (c).

what term best describes segment (overline{qc})?

Explanation:

The steps described are the standard construction for an angle - bisector. An angle - bisector is a ray or segment that divides an angle into two equal angles. In the given construction, point \(C\) is found by intersecting arcs drawn from points \(A\) and \(B\) (which are on the sides of the angle \(\angle PQR\)) and then segment \(QC\) is drawn from the vertex \(Q\) to \(C\). This segment \(QC\) divides \(\angle PQR\) into two equal angles.

Answer:

angle - bisector