
List of Axioms, Definitions, and Theorems
... which originates from a common endpoint of h and h0 then (hkh0 ) and therefore hk + kh0 = β. Definition (2.4.2). An angle is called right if its measure is equal to half that of a straight angle. An acute angle is an angle with measure less than that of a right angle, and an obtuse angle is an angle ...
... which originates from a common endpoint of h and h0 then (hkh0 ) and therefore hk + kh0 = β. Definition (2.4.2). An angle is called right if its measure is equal to half that of a straight angle. An acute angle is an angle with measure less than that of a right angle, and an obtuse angle is an angle ...
SMSG Geometry Summary
... 4. We do not write = between two geometric figures unless we mean the figures are exactly the same. Example: Two descriptions of exactly the same angle or exactly the same line using different points. 5. Definition. Given a correspondence ABC ←→ DEF between the vertices of two triangles. If every pa ...
... 4. We do not write = between two geometric figures unless we mean the figures are exactly the same. Example: Two descriptions of exactly the same angle or exactly the same line using different points. 5. Definition. Given a correspondence ABC ←→ DEF between the vertices of two triangles. If every pa ...
SMSG Geometry Summary
... 4. We do not write = between two geometric figures unless we mean the figures are exactly the same. Example: Two descriptions of exactly the same angle or exactly the same line using different points. 5. Definition. Given a correspondence ABC ←→ DEF between the vertices of two triangles. If every pa ...
... 4. We do not write = between two geometric figures unless we mean the figures are exactly the same. Example: Two descriptions of exactly the same angle or exactly the same line using different points. 5. Definition. Given a correspondence ABC ←→ DEF between the vertices of two triangles. If every pa ...
2.1 - UCR Math Dept.
... kUse the following equation _____________________ where k is an integer.k Example 4: (Finding measures of coterminal angles) Find the smallest possible positive angle that are coterminal with the following angles: a) ...
... kUse the following equation _____________________ where k is an integer.k Example 4: (Finding measures of coterminal angles) Find the smallest possible positive angle that are coterminal with the following angles: a) ...
7•2 Naming and Classifying Polygons and Polyhedrons
... A polygon is a closed figure that has three or more sides. Each side is a line segment, and the sides meet only at the endpoints, or vertices. This figure is a polygon. ...
... A polygon is a closed figure that has three or more sides. Each side is a line segment, and the sides meet only at the endpoints, or vertices. This figure is a polygon. ...
Steinitz's theorem

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices). That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who submitted its first proof for publication in 1916. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name ""Steinitz's theorem"" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑