Kobon Triangle -- from Wolfram MathWorld

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore defined as one of the triangles constructed in such a way. The first few terms are 1, 2, 5, 7, 11, 15, 21, (OEIS A006066). It appears to be very difficult to find an analytic expression for the nth term, although Saburo Tamura has proved an upper bound on N(n) of |_n(n-2)/3_|, where |_x_| is the floor function (Eppstein).

computational geometry - How to draw Kobon triangles - Mathematica Stack Exchange

Obtuse Triangle -- from Wolfram MathWorld

Triangle -- from Wolfram MathWorld

Central Triangle -- from Wolfram MathWorld

Gergonne Line -- from Wolfram MathWorld

UnitTriangle—Wolfram Language Documentation

PDF) Congruent triangles in arrangements of lines

Fuhrmann Triangle -- from Wolfram MathWorld

Altitude -- from Wolfram MathWorld

How to draw a Pascal triangle up to n=20 - Quora

Obtuse Triangle -- from Wolfram MathWorld

Kobon Triangle -- from Wolfram MathWorld