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 converge on the Sierpinski triangle. This is what is happening with the triangle above, but any other set would suffice. If one takes a point and applies each of the transformations "d", "d", and "d" to it randomly, the resulting points will be dense in the Sierpinski triangle, so the following algorithm will again generate arbitrarily close approximations to it: Start by labeling p, p and p as the corners of the Sierpinski triangle, and a random point v. Set , where "r" is a random number 1, 2 or 3. Draw the points v to v. If the first