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# Chapter 7 Notecards

Term | Definition |
---|---|

Pythagorean Theorem | In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs |

Pythagorean Triple | a set of three positive integers a, b, and c that satisfy the equation c2 = a2 + b2. The most common ones are: (3,4,5), (5,12,13), (8,15,17), (7,24,25) |

Converse of Pythagorean Theorem | if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. |

Theorem 7.3 | 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 |

Theorem 7.4 | 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 other two sides, then the triangle is an obtuse triangle |

Theorem 7.5 | 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 |

Geometric Mean (Altitude) Theorem | In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments. |

Geometric Mean (Leg) Theorem | the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. |

45-45-90 Theorem | The hypotenuse is square root 2 times as long as each leg |

30-60-90 Theorem | the hypotenuse is twice as long as the shorter leg, and the longer leg is square root 3 times as long as the shorter leg |

Trigonometric Theorem | a ratio of the lengths of two sides in a right triangle. |

Tangent | The ratio of the lengths of the legs in a right triangle is constant for a given angle measure |

Tangent Ratio | a trigonometric ratio, abbreviated as tan, for a right triangle ABC the tangent of <A (written as tan A) is defined as: tan A= length of leg opposite <A / length of leg adjacent to <A |

Sine | A trigonometric ratio, abbreviated as sin. |

Cosine | A trigonometric ratio, abbreviated as cos. For a right triangle |

Sine Ratio | Let triangle ABC be a right triangle w/ acute <A... sin A = length of leg opposite <A / length of hypotenuse |

Cosine Ratio | Let triangle ABC be a right triangle w/ acute <A... cos A = length of leg adjacent to <A / length of hypotenuse |

Angle of Elevation | if you look up at an object, the angle your line of sight makes with a horizontal line. |

Angle of Depression | If you look down at an object, the angle you line of sight makes with a horizontal line |

Solve a Right Triangle | means to find the measures of all of its sides and angles if you have either two side lengths or one side length and the measure of one acute angle. |

Inverse Tangent Ratio | if tan A = x, then tan-1x = m<A |

Inverse Sine Ratio | if sin A= y, then sin-1y = m<A |

Inverse Cosine Ratio | if cos A= z, then cos-1z = m<A |

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