Euler\'s Line

This project is simple but has many moving part to it.  It is designed for a Pre-AP Classroom.  I modified the content to fit a group project atmosphere to encourage collaboration. It can be done over two 45 minute class periods. It can be done as a take home project.  Students should already have a strong Algebraic.  If you would like to modify content to fit a lower level class you give task and require less work shown. Also If you do not have enough people. The Architect and the Historian can be the same person. Constructing the the triangle and lines are the easy part. Finding the the equations of the lines is going to stump many of the students.  This should be at least on major grade.

Standards

7) Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to:

(A) use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

(B) use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and

(C) derive and use formulas involving length, slope, and midpoint.

Credits

https://www.youtube.com/watch?v=ImFJJfrUOuk circumcenter
https://www.youtube.com/watch?v=3_fUBAEzq6o perpendicular bisector
https://www.youtube.com/watch?v=KNGDdXSBkVw centroid and median
https://www.wyzant.com/resources/answers/2717/abc_has_vertices_a_0_6_b_4_6_and_c_1_3_find_the_orthocenter_of_abc_list_your_steps altitude orthocenter.

Other

The Khan Academy has a great video on Euler's line for additional information.
https://www.khanacademy.org/math/geometry/triangle-properties/triangle_property_review/v/euler-line