In Modern Geometries, we discussed ways that Euclid's Parallel Postulate fails in other geometries. This worksheet shows one of the ways it fails in hyperbolic geometry, the explanation is in the text box on the actual worksheet - it also shows an ideal triangle.[br][br]Ideal triangles have every vertex at an ideal point (at infinity), whose interior angles are all 0. Due to the vertices all being at infinity in the Poincare disk, the perimeter is infinite, causing it to be the largest possible triangle in hyperbolic geometry. All ideal triangles are congruent.