# Really cool: Explore Triangle Centers

## Explore Triangle Centers

Centroid, Orthocenter, Incenter, Circumcenter Observe the relationships of special segments of triangles and their points of concurrency. The INCENTER (I) is the point of concurrency of the angle bisectors. The CIRCUMCENTER (C) is the point of concurrency of the perpendicular bisectors. The CENTROID (G) is the point of concurrency of the medians and is the center of gravity. The ORTHOCENTER (H) is the point of concurrency of the altitudes. The Euler segment and Euler line are formed by C, H, and G.
1. Walking the edge of this inner triangle is the shortest path between the segments AB, BC, and CA.
2. Can you think of a situation in real life when you might want to find the shortest path between the sides of a triangle?
18)  Which of the inner triangles is similar to Triangle ABC? 19)  Is the Centroid of Triangle ABC also the centroid of the inner centroid triangle? 20)  What would happen if you continued to draw centroid triangles inside centroid triangles? Would they always be similar?