Discovery Learning Notes
... will be called points and will often be denoted by the letters P, Q, and R (though the set of points may be infinite). Specific subsets of U will be called lines and we will denote lines by `, `1 , and `2 (though again there might be an infinite number of lines). It is usually our axioms that tell u ...
... will be called points and will often be denoted by the letters P, Q, and R (though the set of points may be infinite). Specific subsets of U will be called lines and we will denote lines by `, `1 , and `2 (though again there might be an infinite number of lines). It is usually our axioms that tell u ...
Prove Triangles Congruent by ASA & AAS
... ASA Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles & included side of a second triangle, then the two triangles are congruent AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corre ...
... ASA Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles & included side of a second triangle, then the two triangles are congruent AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corre ...
Polygon Classification
... The easiest way to identify the polygon is to identify which shapes are not polygons. B and C each have at least one curved side, so they cannot be polygons. D has all straight sides, but one of the vertices is not at the endpoint of the adjacent side, so it is not a polygon either. A is the only po ...
... The easiest way to identify the polygon is to identify which shapes are not polygons. B and C each have at least one curved side, so they cannot be polygons. D has all straight sides, but one of the vertices is not at the endpoint of the adjacent side, so it is not a polygon either. A is the only po ...
Angles of Triangles
... however, other angles are formed The original 3 angles of the triangle are the interior angles The angles that are adjacent to interior angles are the exterior angles Each vertex has a pair of exterior angles ...
... however, other angles are formed The original 3 angles of the triangle are the interior angles The angles that are adjacent to interior angles are the exterior angles Each vertex has a pair of exterior angles ...
1 Solution of Homework
... 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases, with 0, 1, 2, 3, 4 common tangents. Describe how they arise. Answer. For any two different circles, there are five possibilities regarding their common tangents: (0) On ...
... 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases, with 0, 1, 2, 3, 4 common tangents. Describe how they arise. Answer. For any two different circles, there are five possibilities regarding their common tangents: (0) On ...
i. all 3 medians of the triangle
... 3. Choose a location for the amusement park based on the work you did in part 2. Explain why you chose this point. Solution Answers will vary, but it is critical for students to have a mathematical justification for their decision. For example, they may choose the circumcenter because it is equidis ...
... 3. Choose a location for the amusement park based on the work you did in part 2. Explain why you chose this point. Solution Answers will vary, but it is critical for students to have a mathematical justification for their decision. For example, they may choose the circumcenter because it is equidis ...
File - Analytic Geometry
... Warm-up Begin at the word “Tomorrow”. Every Time you move, write down the word(s) upon which you land. ...
... Warm-up Begin at the word “Tomorrow”. Every Time you move, write down the word(s) upon which you land. ...
Geometry - Henrico County Public Schools
... line. Compare the slopes to determine whether two lines are parallel, perpendicular, or neither. Determine whether a figure has point symmetry, line symmetry, both, or neither. Given an image and pre-image, identify the transformation that has taken place as a reflection, rotation, dilation, o ...
... line. Compare the slopes to determine whether two lines are parallel, perpendicular, or neither. Determine whether a figure has point symmetry, line symmetry, both, or neither. Given an image and pre-image, identify the transformation that has taken place as a reflection, rotation, dilation, o ...
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 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑