Geometry Theorems 8 Right Triangles
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Created by:
PAHStudent1 on August 7, 2012
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English | Math / Symbols |
|---|---|
 Theorem 8-1 | The altitude is drawn to the hypotenuse of a right ∆, then the two ∆s formed are ∼ to the original ∆ and to each other. |
| Theorem 8-1 corollary 1 | When the altitude is drawn to the hypotenuse of a right ∆, the length of the altitude is the geometric mean between the segments of the hypotenuse. |
| Theorem 8-1 corollary 2 | When the altitude is drawn to the hypotenuse of a right ∆, each leg is the geometric mean between the hypotenuse and the segments of the hypotenuse that is adjacent to that leg. |
| Theorem 8-2 Pythagorean Theorem | In a right ∆, the square of the hypotenuse is equal to the sum of the squares of the legs. |
| Theorem 8-3 Converse of Pythagorean Theorem | If the square of one side of a ∆ is equal to the sum of the squares of the other two sides, then the ∆ is a right ∆. |
| Common Right Triangle Length | 3,4,5 / 6,8,10 / 9,12,15 / 12,16,20 / 15,20,25 5,12,13 / 10, 24, 26 8, 15, 17 7, 24, 25 |
| Theorem 8-3 | If c² = a² + b², then m∠C = 90, and ∆ ABC is right. |
| Theorem 8-4 | If c² < a² + b², then m∠C < 90, and ∆ ABC is acute. |
| Theorem 8-5 | If c² > a² + b², then m∠C > 90, and ∆ ABC is obtuse. |
| Theorem 8-6 45°-45°-90° Theorem | In a 45°-45°-90° ∆, the hypotenuse is √2 times as long as a leg. |
| Theorem 8-7 30°-60°-90° Theorem | In a 30°-60°-90° ∆, the hypetenuse is twices as long as the shorter let, and the longer leg is √3 as long as the shorter leg. |
| Trigonometry - Tangent Ratio - the ratio of the legs | tangent of ∠A = leg opposite ∠A / leg adjacent to ∠A |
| Trigonometry - Sine Ratio - the ratio that relate the opposite leg to the hypotenuse | sine of ∠A = leg opposite ∠A / hypotenuse |
| Trigonometry - Cosine Ratio - the ratio that relate the adjacent leg to the hypotenuse | cosine of ∠A = leg adjacent to ∠A / hypotenuse |
| Abbreviation | tan A = opposite / adjacent sin A = opposite / hypotenuse cos A = adjacent / hypotenuse |
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