Set square 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles. They are often purchased in packs with protractors and compasses. Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a hinge marked with angles. Adjustment to the marked angle will produce any desired angle up to a maximum of 180°. In many European countries, the most common form of set square combines a 90-45-45 triangle with a protractor into a single tool made of clear plastic. Named "Geodreieck" (German
Triangle group is Euclidean if the angle sum is exactly π, spherical if it exceeds π and hyperbolic if it is strictly smaller than π. Moreover, any two triangles with the given angles are congruent. Each triangle group determines a tiling, which is conventionally colored in two colors, so that any two adjacent tiles have opposite colors. In terms of the numbers "l", "m", "n" > 1 there are the following possibilities. formula_4 The triangle group is the infinite symmetry group of a certain tessellation (or tiling) of the Euclidean plane by triangles whose angles add up to π (or 180°). Up