Medial triangle

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The red triangle is the medial triangle of the black. The endpoints of the red triangle coincide with the midpoints of the black triangle.

The medial triangle of a triangle ABC refers to the triangle with vertices as the midpoints of triangle ABC.

The medial triangle can also be viewed as the image of triangle ABC transformed by a homothety centered at the centroid with ratio -1/2. Hence, the medial triangle is inversely similar and shares the same centroid and medians with triangle ABC.

Note that the orthocenter of the medial triangle coincides with the circumcenter of triangle ABC. This fact provides a tool for proving collinearity of the circumcenter, centroid and orthocenter.

Finally, medial triangle is different from the median triangle.