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urp:triangles
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| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
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urp:triangles [2021-10-15] nerf_herder |
urp:triangles [2021-10-28] nerf_herder |
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| Definitions: | Definitions: | ||
| - | * isosceles - 2 sides the same length | + | * isosceles - (at least) 2 sides the same length, modern definition includes equilateral |
| * equilateral - all 3 sides the same length | * equilateral - all 3 sides the same length | ||
| + | * acute triangle - all angles are < 90 degrees | ||
| + | * obtuse triangle - one angle is > 90 degrees | ||
| * similar triangles - triangles that have same shape (all 3 angles), but size can be different. The sides have same ratios | * similar triangles - triangles that have same shape (all 3 angles), but size can be different. The sides have same ratios | ||
| * congruent triangles - triangles that have the same shape and size | * congruent triangles - triangles that have the same shape and size | ||
| * CPCT - corresponding parts of congruent triangles (are equal) | * CPCT - corresponding parts of congruent triangles (are equal) | ||
| + | |||
| + | __Isosceles triangle__ - base angles are the same, __Equilateral__ - all angles are the same (60°), aka equiangular | ||
| __Centroid of a triangle__ - center (where the lines bisecting each angle will meet) | __Centroid of a triangle__ - center (where the lines bisecting each angle will meet) | ||
| Line 26: | Line 30: | ||
| * SAS - side-angle-side | * SAS - side-angle-side | ||
| * SSS - side-side-side | * SSS - side-side-side | ||
| - | * RHS - right-angle, hypotenuse, side (basically ASS, which doesn't work for acute angles, but does for right-angle). Using Pythagorean theorem can be converted to SSS. | + | * RHS - right-angle, hypotenuse, side, also called HL (hypotenuse & leg). |
| + | * RHS is basically ASS/SSA, which doesn't work for acute angles, but does for right-angle. Using Pythagorean theorem it can be converted to SSS. | ||
| ===Right Triangles=== | ===Right Triangles=== | ||
| - | 45-45-90 triangle: hyp = side * √2 | + | * 45-45-90 triangle: hyp = side * √2 |
| - | 30-60-90 triangle: short side = a, long side = a*√3, hyp = 2a | + | * 30-60-90 triangle: short side = a, long side = a*√3, hyp = 2a |
| + | * 3-4-5 triangle: if a triangle has sides 3n and 4n, then the hypotenuse will be 5n | ||
| __area__ of a right triangle = 1/2*h*w | __area__ of a right triangle = 1/2*h*w | ||
urp/triangles.txt · Last modified: 2021-11-08 by nerf_herder
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