Angles in the same segment are equal.
This pretty theorem details of the construct of triangles using well known I/GCSE circle theorems (Exterior Angle of Triangle and Cyclic Quadrilateral). I like the petal effect in the middle. Never come across the word species in conjunction with triangles before.
Geometric Progressions, essential for Core AS mathematicians, appear in Victorian textbook, Synopsis of Elementary Results. In the case where the sum to infinity exists, there is a nice proof by similar triangles.
Euclid Book II proposition 9 and 10 proved by area decomposition marries algebra and geometry with a recipe for making Tartans.