Euclidean geometry equal (SAS), or two angles and a side equal (ASA) (Book I, propositions 4, 8, and 26). Triangles with three equal angles (AAA) are similar, but not necessarily congruent. Also, triangles with two equal sides and an adjacent angle are not necessarily equal or congruent. The sum of the angles of a triangle is equal to a straight angle (180 degrees). This causes an equilateral triangle to have three interior angles of 60 degrees. Also, it causes every triangle to have at least two acute angles and up to one obtuse or right angle. The celebrated Pythagorean theorem (book I,
Sierpinski triangle the Sierpinski triangle. The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets: Each removed triangle (a "trema") is topologically an open set. This process of recursively removing triangles is an example of a finite subdivision rule. The same sequence of shapes, converging to the Sierpinski triangle, can alternatively be generated by the following steps: Note that this infinite process is not dependent upon the starting shape being a triangle—it is just clearer that way. The first few steps starting, for example, from a square also tend towards a Sierpinski triangle. Michael Barnsley used