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| the geometric mean of two numbers is the positive square root of their product |
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The geometric mean of two positive numbers a and b is the number x such that:
a/x = x/b . So, x² = ab |
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| If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. |
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| The altitude drawn to the hypotenuse of a right triangle seperates the hypotenuse into two segments, The length of this altitude is the geometric mean between the lengths of those two segments. |
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| The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. the length of a leg of this triangle is the geometric mean between the l[ength of the hypotenuse and the segment of the hypotenuse adjacent to that leg. |
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| In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. |
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| set of three non-zero whole numbers a, b, and c, such that a²+b²=c². |
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Common Pythagorean Triples:
3,4,5
3x,4x,5x
5,12,13
5x,12x,13x
8,15,17
8x,15x,17x
7,24,25
7x,24x,25x |
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| If the sum of the squares of the lengths of the shortest sides of a triangle is equal to the square of the length of the shortest side, then the triangle is a right triangle. |
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| If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle. |
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| If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the two other sides, then the triangle is an obtuse triangle. |
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| the location of a point in space |
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| In a 45-45-90 triangle, the legs l are congruent and the length of the hypotenuse h is √2 times the length of a leg. |
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| In a 30-60-90 triangle, the lenth of the hypotenuse h is 2 times the length of the shorter leg ssled and the lenth of the longer leg lleg is √3 times the length of sleg. |
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| study of the measures of triangles |
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| ratio of the lengths of two sides of a right triangle. |
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| sine = opposite over hypotenuse |
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| cosine = adjacent over hypotenuse |
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| tangent= opposite over adjacent |
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| the angle whose sine is x. |
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| the angle whose cosine is x. |
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| the angle whose tangent is x. |
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| angle formed by a horizonal line and an observer's line of sight to an object above the horizontal line |
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| angle formed by a horizontal line and an observer's line of sight to an object that is below the horizontal line. |
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| used to find lengths and angle measures for any triangle |
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law of sine
sinA sinB sinC
---- = ---- = ----
a b c |
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Law of Cosines:
a²= b² + c² - 2bc(cosA)
b²= a² + c² - 2ac(cosB)
c²= a² + b² - 2ab(cosC) |
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| Used to find triangles if you know the measures of two sides and an included angle. |
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| the case in which triangles are determined? |
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| describes both magnitude and direction of a quantity |
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| length of vector from initial point to its terminal point |
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| the angle that it forms with the horizontal line or as a meaurement between 0 and 90 on a north-south east-west line |
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| sum of two or more vectors |
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| one method to add vectors |
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| another method to add vectors |
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| if the initial point of the vector is at the origin. |
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to describe a vector with any initial point, use this, which describes the vector in terms of its horizontal component x an vertical component y
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If a,b and c,d are vectors and k is a scalar, then the following are true.
a,b + c,d = a+c,b+d
a,b - c,d = a-c, b-d
k(a,b) = ka, kb |
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