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If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school ...
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with n sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for n sides ...
A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if =, where r, s, k ≥ 0 and where the p i are distinct Pierpont primes greater than 3 (primes of the form +). [8]: Thm. 2 These polygons are exactly the regular polygons that can be constructed with Conic section, and the regular polygons ...
A simple polygon is the boundary of a region of the plane that is called a solid polygon. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon.
The regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number of vertices and edges.
Pages in category "Simple machines" The following 19 pages are in this category, out of 19 total. This list may not reflect recent changes. ...
Similar to boundary representation, the surface of the object is represented. However, rather than complex data structures and NURBS, a simple surface mesh of vertices and edges is used. Surface meshes can be structured (as in triangular meshes in STL files or quad meshes with horizontal and vertical rings of quadrilaterals), or unstructured ...
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