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urp:angles
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urp:angles [2021-10-21] nerf_herder |
urp:angles [2021-11-08] (current) nerf_herder |
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| - | ==== Angles and Vectors ==== | + | ===== Angles and Vectors ===== |
| - | === Angles and Lines=== | + | ==== Angles and Lines==== |
| {{ :urp:angles.jpg?250|}} | {{ :urp:angles.jpg?250|}} | ||
| - | * __Complementary angles__ add up to 90' | + | * **Complementary angles** add up to 90' |
| - | * __Supplementary angles__ add up to 180' | + | * **Supplementary angles** add up to 180' |
| - | * __alternative angles__ are equal (congruent angles on transversal line intersecting two parallel lines) | + | * **alternative angles** are equal (congruent angles on transversal line intersecting two parallel lines) |
| - | * __vertical angles theorem__ says that angles opposite one another when two straight lines intersect are congruent | + | * **vertical angles theorem** says that angles opposite one another when two straight lines intersect are congruent |
| In the diagram shown, <b₁ and <c are complementary, as are <e and <f. Angles <b₁ and <d are supplementary. Because of alternative angles of parallel lines, <b₂ = <b', and <d = <d' (assuming lines Y and Z are parallel). From the vertical angles theorem, <b₁ = <b₂. | In the diagram shown, <b₁ and <c are complementary, as are <e and <f. Angles <b₁ and <d are supplementary. Because of alternative angles of parallel lines, <b₂ = <b', and <d = <d' (assuming lines Y and Z are parallel). From the vertical angles theorem, <b₁ = <b₂. | ||
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| Distance between two points = √(Δx² + Δy²) (based on Pythagorean theorem) | Distance between two points = √(Δx² + Δy²) (based on Pythagorean theorem) | ||
| - | === Vectors (Rays) === | + | ==== Vectors (Rays) ==== |
| Length of a vector can be written as ||v|| (the "norm" of vector v) | Length of a vector can be written as ||v|| (the "norm" of vector v) | ||
| Distance of two vectors: first add the vectors to make a combined vector. To add vectors, simply add each part of the vector, ie. (x1 + x2, y1 + y2) | Distance of two vectors: first add the vectors to make a combined vector. To add vectors, simply add each part of the vector, ie. (x1 + x2, y1 + y2) | ||
| + | ------ | ||
| Go back to [[geometry]] or [[math]] page. | Go back to [[geometry]] or [[math]] page. | ||
urp/angles.txt · Last modified: 2021-11-08 by nerf_herder
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