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# Triangles

### Theorems and definitions

Question | Answer |
---|---|

Similar Triangles Theorem | 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 △CBD ~ ￼ABC △￼ACD~￼ABC △￼CBD~￼ACD |

Corollarry 1 | when the altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric mean between the segments of the hypotenuse |

Corollary 2 | when the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg |

Pythagorean Theorem | In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs C²=a²+b² |

Pythagorean Triple | Is a set of three positive integers a, b, and c that satisfy the equation C²=a²+b² |

Converse of the 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 if C^2=a^2+b^2 then (triangle)ABC is a right triangle |

Acute Triangles Theorem | 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 acute. C^2<a^2+b^2 |

Obtuse Triangle Theorem | 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 obtuse C²>a²+b² |

45⁰- 45⁰ - 90⁰ | In a 45 45 90 triangle, the hypotenuse is root 2 times as long as each leg |

60⁰-90⁰ | the hypotenuse is 2 times as long as the shorter leg and the longer leg is root 3 times as long as shorter leg |

Trigonometric Ratios | sin= side opposite <A / hypotenuse = a/c cos= side adjacent <A / hypotenuse = b/c tan= side opposite <A / side adjacent <A = a/b |

Angle Elevation | is the angle that your line of sight makes with a horizontal line when you stand and look up at a point in the distance |

Triangle Sum Theorem | the sum of the measure of the interior angles of a triangle is 180⁰ |

Exterior Angles Theorem | The measure of an exterior angle of a triangle is equal to the sum of the measures of two non-adjacent interior angels |

Third Angles Theorem | If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent |

Side Side Side Congruence Postulate (SSS) | If three sides of one triangle are congruent to three sides of second triangle, then the two triangles are congruent |

Side Angle Side (SAS) Congruence Postulate | If two dies and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent |

Angle Side Angle (ASA) Congruence Postulate | If two angles and he included side of one triangle is congruent to two angles and the included side of a second triangle, then the two triangles are congruent |

Angle Angle Side (AAS) Congruence Theorem | If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent |

Corresponding Parts of Congruent Triangles are Congruent (CPCTC) | If two triangles are congruent, then all corresponding parts f those triangles are also congruent |

Base Angle | two angles that are adjacent to the base of the triangle |

Base Angles Theorem | If two sides of a triangles are congruent, then the angles opposite them are congruent |

Corollary to the Base Angles Theorem | If a triangle is equilateral, then it is equiangular |

Corollary to Theorem | If a triangle is equiangular, then it is equilateral |

Hypotenuse-Leg (HL) Congruence Theorem | If the hypotenuse and a leg of a right (RT) triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent |

Created by:
McChicklet