In geometry, two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent (i.e., they intersect at a single point). This is a symmetric property; that is, if the perpendiculars from the vertices A, B, C of triangle △ABC to the sides EF, FD, DE of triangle △DEF are concurrent then the perpendiculars from the vertices D, E, F of △DEF to the sides BC, CA, AB of △ABC are also concurrent. The points of concurrence are known as the orthology centres of the two triangles.^[1][2]

The following are some triangles associated with the reference triangle ABC and orthologic with it.^[3]

• Medial triangle
• Anticomplementary triangle
• Orthic triangle
• The triangle whose vertices are the points of contact of the incircle with the sides of ABC
• Tangential triangle
• The triangle whose vertices are the points of contacts of the excircles with the respective sides of triangle ABC
• The triangle formed by the bisectors of the external angles of triangle ABC
• The pedal triangle of any point P in the plane of triangle ABC

Sondat's theorem states that If two triangles ABC and A'B'C' are perspective and orthologic, then the center of perspective P and the orthologic centers Q and Q' are on the same line perpendicular to the axis of perspectivity ^{[4]: Thm. 1.6}

Sondat's theorem