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urp:geometry [2021-10-13] nerf_herder |
urp:geometry [2021-11-17] (current) nerf_herder |
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| * [[Angles|Angles and Vectors]] | * [[Angles|Angles and Vectors]] | ||
| - | * [[Polygons]] | ||
| * [[Triangles]] | * [[Triangles]] | ||
| * [[Circles|Circles, Chords, etc]] | * [[Circles|Circles, Chords, etc]] | ||
| - | * [[Graphing|Graphing curves, circles, etc.]] | + | * [[Polygons]] |
| - | + | ||
| - | ====Polygons==== | + | === misc === |
| - | + | Truth tables: | |
| - | The __sum of angles in a polygon__ = 180 (n - 2), where n = number of sides. This can also be written as: 180 + 180 (n-3). (Basically you add in another triangle when adding a side to polygon) | + | first columns : True/False values of the variables, such as p, q, or p' or ~p for inverse values. Next columns are logic combinations of the variables |
| - | + | ||
| - | ====Circles==== | + | |
| - | + | ||
| - | * __chord__ has two endpoints on a circle | + | |
| - | * __secant__ is a line that contains a chord, but extends beyond the circle | + | |
| - | * __Intercepted arc__ is the part of the circle contained within the two lines | + | |
| - | * __Central angle__ is angle of two lines from the center of the circle | + | |
| - | * __Inscribed/Interior angle__ has two points and the vertex all on the circle itself | + | |
| - | * __central angle__ is same as the degrees of intercepted arc | + | |
| - | + | ||
| - | if two chords AB, CD intersect at P, then AP * PB = CP * PD | + | |
| - | + | ||
| - | Interior angle = 1/2 of intercepted arc | + | |
| - | all inscribed angles going to the two same points on the circle have the same angle | + | |
| - | angle of intersecting secants theorem: | + | |
| - | angle formed by the secant intersection = (opposite arc - adjacent arc)/2 | + | |
| - | + | ||
| - | An angle outside the circle with two secants (or tangents) will have an angle | + | |
| - | that is 1/2 * (difference of the intercepted arcs) | + | |
| - | coterminal angle - the rest of the circle outside the angle. | + | | p | q | p ⋂ q | p ⋃ q| p => q | |
| - | eg. angle of 30', the coterminal is 330' | + | | T | T | T | T | T | |
| - | in radians, use the absolute value. | + | | T | F | F | T | F | |
| - | 2pi - |angle|, or |angle| - 2pi for the negative angle | + | | F | T | F | T | T | |
| + | | F | F | F | F | T | | ||
| + | p => q means condition p implies condition q. If p is true, then an implication can be drawn or not, depending on q. If p is false, then an implication cannot be ruled out, regardless of q, so it is left as true. | ||
| - | area of an arc: | ||
| - | a = rad*r²/2 .... comes from a = πr² for full circle, and the | ||
| - | proportion of a circle in the arc is rad/2π | ||
| - | so a = (rad/2π)*(πr²) | ||
| === See Also === | === See Also === | ||
| - | * https://www2.clarku.edu/faculty/djoyce/trig/identities.html | ||
| * 11 pages of definitions, postulates and theorems: http://www.ouchihs.org/ourpages/auto/2013/7/26/52822673/Geo-PostulatesTheorems-List.pdf | * 11 pages of definitions, postulates and theorems: http://www.ouchihs.org/ourpages/auto/2013/7/26/52822673/Geo-PostulatesTheorems-List.pdf | ||
| Back to [[math]] page. | Back to [[math]] page. | ||
urp/geometry.1634102675.txt.gz · Last modified: 2021-10-13 by nerf_herder
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