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Sonic Geometry: Difference between revisions
→Octagon 1080 Degrees
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==Triangle 180 Degrees== | ==Triangle 180 Degrees== | ||
[[File:Regular polygon 3 annotated.svg|thumb|Equilateral triangle with annotation.]] | [[File:Regular polygon 3 annotated.svg|thumb|Equilateral triangle with annotation.]] | ||
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. An equilateral triangle has three sides of the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. <ref>[https://en.wikipedia.org/wiki/Triangle Triangle wiki]</ref> | A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. An equilateral triangle has three sides of the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise. In rigorous treatments, a triangle is therefore called a 2-simplex (see also Polytope). Elementary facts about triangles were presented by Euclid, in books 1–4 of his Elements, written around 300 BC. | ||
The measures of the interior angles of the triangle always add up to 180 degrees (same color to point out they are equal). The sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees. This fact is equivalent to Euclid's parallel postulate. This allows determination of the measure of the third angle of any triangle, given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees. | |||
<ref>[https://en.wikipedia.org/wiki/Triangle Triangle wiki]</ref> | |||
==Square 360 Degrees== | ==Square 360 Degrees== | ||
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==Octagon 1080 Degrees== | ==Octagon 1080 Degrees== | ||
[[File:Regular polygon 8 annotated.svg|thumb|Regular octagon with annotation.]] | [[File:Regular polygon 8 annotated.svg|thumb|Regular octagon with annotation.]] | ||
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. | In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. | ||