Centroids and Orthocenters

Author:: Bryan Christian

Topic:: Centroid or Barycenter, Geometry, Median Line, Orthocenter

Centroid of a triangle

The median of a triangle connects a vertex with the midpoint of the opposite side. In the triangle below: 1) use the point tool to create the midpoint of each side of the triangle; 2) use the line tool to create a segment connecting each midpoint with the opposite vertex. The points where the medians intersect is the centroid of the triangle. Use the move tool (the arrow), to move one of the vertices. Note the location of the centroid when the triangle is: 4) acute; 5) obtuse; 6) right-angled.

Are the medians concurrent?

Select all that apply

A
Yes
B
No

Check my answer (3)

If the triangle is acute, where is the centroid?

Select all that apply

A
inside the triangle
B
outside the triangle
C
on the triangle

Check my answer (3)

If the triangle is obtuse, where is the centoid?

Select all that apply

A
inside the triangle
B
outside the triangle
C
on the triangle

Check my answer (3)

If the triangle is a right-angled triangle, where is the centroid?

Select all that apply

A
inside the triangle
B
outside the triangle
C
on the triangle

Check my answer (3)

Orthocenter

The altitude of a triangle is the segment perpendicular to one side of a triangle to the opposite vertex. In the triangle below use the perpendicular line tool to: 1) create a perpendicular to side AB through C (select the perpendicular tool, then select side AB, then C); 2) create a perpendicular to side AC through B; 3) create a perpendicular to side BC through A. The points where the altitudes intersect is the orthocenter of the triangle. Use the move tool (the arrow), to move one of the vertices. Note the location of the orthocenter when the triangle is: 4) acute; 5) obtuse; 6) right-angled.