Students will learn about the centroid and orthocenter, two of the four centers of triangles. First, students will learn what medians are, then what the centroid is, then what the centroid theorem says. After that, they'll learn what the orthocenter is. Students should see that the centroid always lies inside the triangle, while the orthocenter lies inside acute triangles, outside obtuse triangles, and on the boundary of right triangles. Here's a video on the centroid and orthocenter. Next, students will learn how to find the orthocenter given the coordinates of a triangle's vertices. Finally, students will learn why the three medians cut a triangle into six triangles of equal area (video).

Conclude by giving your students these challenges:

- Happy Octopus by NRICH
- Triangle Numbers by NRICH
- Painted Faces by NRICH
- An Unhappy End by NRICH