Chapter 4: Congruent Triangles
... 32. JKL is isosceles with KJ LJ. JL is five less than two times a number. JK is
three more than the number. KL is one less than the number. Find the
measure of each side.
33. ROAD TRIP The total distance from Charlotte to
Raleigh to Winston-Salem and back to Charlotte
is about 292 miles. The dist ...
Axioms of Incidence Geometry Incidence Axiom 1. There exist at
... Postulate 9 (The SAS Postulate). If there is a correspondence between the vertices of two triangles such that two sides and the included
angle of one triangle are congruent to the corresponding sides and angle of the other triangle, then the triangles are congruent under that
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers. The name of these embeddings is French for a ""child's drawing""; its plural is either dessins d'enfant, ""child's drawings"", or dessins d'enfants, ""children's drawings"".Intuitively, a dessin d'enfant is simply a graph, with its vertices colored alternating black and white, embedded in an oriented surface that, in many cases, is simply a plane. For the coloring to exist, the graph must be bipartite. The faces of the embedding must be topological disks. The surface and the embedding may be described combinatorially using a rotation system, a cyclic order of the edges surrounding each vertex of the graph that describes the order in which the edges would be crossed by a path that travels clockwise on the surface in a small loop around the vertex.Any dessin can provide the surface it is embedded in with a structure as a Riemann surface. It is natural to ask which Riemann surfaces arise in this way. The answer is provided by Belyi's theorem, which states that the Riemann surfaces that can be described by dessins are precisely those that can be defined as algebraic curves over the field of algebraic numbers. The absolute Galois group transforms these particular curves into each other, and thereby also transforms the underlying dessins.For a more detailed treatment of this subject, see Schneps (1994) or Lando & Zvonkin (2004).