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# Geometry Chapter 4

### Geometry Chapter 5

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

triangle | polygon with 3 sides and 3 angles |

scalene triangle | no congruent sides |

isosceles triangle | at least 2 congruent sides |

equilateral triangle | 3 congruent sides and angles (60 degrees) |

acute | 3 angles less than 90 degrees |

right | one angle is 90 degrees, the other two are acute |

obtuse | one angle is more than 90 degrees, the other two are acute |

equiangular | 3 congruent angles |

congruent triangles... | fit on top of each other |

CPCTC | corresponding parts of congruent triangles are congruent |

SSS | side, side, side |

SAS | side, angle, side (angle in between congruent sides) |

ASA | angle, side, angle (side in between congruent angles) |

AAS | angle, angle, side (side is not between congruent angles) |

hypotenuse | opposite right angle, longest side of triangle |

legs | 2 congruent sides of isosceles triangle |

SAS --> | LL |

ASA --> | LA |

ASS --> | HL |

AAS --> | LA or HA |

the sum of the measures of the angles of a triangle = | 180 degrees |

if 2 angles of one triangle are congruent to 2 angles of another triangle, then | the third angles are congruent |

remote interior angles | farthest away from exterior angle, sum equals the exterior angle |

exterior angles | angle formed from a line extended out from the base of a triangle (makes linear pair with non-remote interior angle) |

corollary | a statement that can easily be proven using a theorem (in between a postulate and a theorem) |

proof with angles or segments in the prove | last step is CPCTC |

proof with triangles in the prove | last step is a reason like SAS or AAS, etc. |

2 steps needed in every right triangle proof | def of perpendicular, and def of right triangle |

base | noncongruent side of isosceles triangle |

vertex | where the legs intersect |

base angles | formed where legs intersect base, congruent |

steps in coordinate geometry proof | 1. draw an accurate figure on graph 2. use tools to make necessary calculations 3. write a conclusion based on your results |

tips for drawing a good diagram for a coordinate geometry proof | use as many zeroes as possible, use as few variables as possible |

distance formula | length, equal, congruent in prove |

slope formula | parallel, perpendicular, right angle in prove |

midpoint formula | half, bisect in prove |

overlapping triangle proof tips | use more than 1 pair of congruent triangles, first pair uses given symbols/information, redraw triangles you are using separated, use CPCTC sometimes more than once, look for common sides or angles |