1. The term is **perpendicular bisector**: a line, ray, or segment that divides a segment into two congruent parts at a 90° angle. 2. The term is **angle bisector**: a line, ray, or segment that divides an angle into two congruent parts. 3. The term is **median**: a segment that connects a vertex to the midpoint of the opposite side. 4. The term is **altitude**: a segment that connects a vertex to the opposite side so that it creates a 90° angle. 5. The point where the perpendicular bisectors intersect is the **circumcenter**. 6. The point where the angle bisectors intersect is the **incenter**. 7. The point where the medians intersect is the **centroid**. 8. The point where the altitudes intersect is the **orthocenter**. 9. Given G is the circumcenter, AG equals GB because the circumcenter is equidistant from the vertices of the triangle. Since GB = 21, then AG = 21. 10. DC is given as 16, and BC is twice DC because D is the midpoint of BC (since DC is half of BC). So, BC = 2 \times 16 = 32. 11. GF is given as 19, so GF squared is $$19^2 = 361$$. 12. To find DG, since G is the circumcenter and D is midpoint of BC, DG equals GB minus DB. Since GB = 21 and DB = DC = 16, DG = 21 - 16 = 5. Final answers: - AG = 21 - BC = 32 - GF^2 = 361 - DG = 5