Arttu followed the following instructions:Draw an angle using a straightedge with vertex point QQ . Place points PP and RR at the end of the angle forming segments QP¯¯¯¯¯¯¯¯QP¯ and QR¯¯¯¯¯¯¯¯QR¯ .Using a compass, draw an arc that intersects both sides of the angle. Place two points, AA and BB , at the intersection of the arc with both sides of the angle.Placing the pointed end of the compass on point AA , 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 BB , draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.Place point CC at the intersection of the two smaller arcs and draw a segment from the vertex point QQ to point CC .What term best describes segment QC¯¯¯¯¯¯¯¯QC¯ ?

Question

Arttu followed the following instructions:Draw an angle using a straightedge with vertex point  QQ . Place points  PP  and  RR  at the end of the angle forming segments QP¯¯¯¯¯¯¯¯QP¯  and QR¯¯¯¯¯¯¯¯QR¯ .Using a compass, draw an arc that intersects both sides of the angle. Place two points,  AA  and  BB , at the intersection of the arc with both sides of the angle.Placing the pointed end of the compass on point  AA , 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  BB , draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.Place point  CC  at the intersection of the two smaller arcs and draw a segment from the vertex point  QQ  to point  CC .What term best describes segment  QC¯¯¯¯¯¯¯¯QC¯ ?
midpointmidpointan arcan arcangle bisectorangle bisectorsegment bisector

GPT-4o mini · Answer

The term that best describes segment $ QC $ is **angle bisector**. To elaborate, the angle bisector is a line segment that divides an angle into two equal angles. In Arttu's construction, segment $ QC $ is drawn from the vertex $ Q $ to the intersection point $ C $ of the two smaller arcs. Since $ C $ is constructed such that the arcs from points $ A $ and $ B $ are created to intersect inside the angle, segment $ QC $ indeed bisects the angle formed by segments $ QP $ and $ QR $.