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# WHS Ch 5 - Triangles

### WHS Chapter 5 Properties/Attributes of Triangles

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

acute triangle | triangle with all three angles < 90° |

right triangle | triangle with one 90° angle |

obtuse triangle | triangle with one angle > 90° |

angle bisector | a line or ray that divides an angle into two congruent angles |

conclusion | the phrase following the word 'then' in a conditional statement |

leg of a right triangle | one of the two sides that form the right angle in a right triangle |

perpendicular bisector of a segment | a line that is perpendicular to a segment at its midpoint |

altitude of a triangle | a perpendicular segment from a vertex to the line containing the opposite side |

centroid of a triangle | the point of concurrency of the three medians of a triangle; also known as the center of gravity |

circumcenter of a triangle | the point of concurrency of the perpendicular bisectors of a triangle |

concurrent | three or more lines that intersect at one point |

equidistant | the same distance from two or more objects |

incenter of a triangle | the point of concurrency of the three angle bisectors of a triangle |

median of a triangle | a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side |

midsegment of a triangle | a segment that joins the midpoints of two sides of the triangle |

orthocenter of a triangle | the point of concurrency of the three altitudes of a triangle |

polygon | a closed plane figure formed by three or more line segments |

bisect | cuts or divides something into two equal parts |

slope | the measure of the steepness of a line |

intersection | the set of points that two or more lines have in common |

trinomial | polynomial with 3 terms |

equiangular triangle | triangle with three equal measures |

perimeter | distance around a figure |

deductive reasoning | using logic to draw conclusions from facts, definitions, and properties |

circumference | distance around a circle |

coplanar | points in the same plane |

translation | movement across a plane |

midsegment triangle | the triangle formed by the three midsegments of a triangle |

locus | a set of points that satisfies a given condition |

Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment |

Converse of the Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |

Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. |

Converse of the Angle Bisector Theorem | If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle. |

point of concurrency | a point where three or more lines coincide |

Circumcenter Theorem | The circumcenter of a triangle is equidistant from the vertices of the triangle. |

inscribed | When a circle in a polygon intersects each line that contains a side of the polygon at exactly one point |

circumscribed | when a circle contains all the vertices of a polygon |

Incenter Theorem | The incenter of a triangle is equidistant from the sides of the triangle. |

Centroid Theorem | The centroid of a triangle is located ⅔ of the distance from each vertex to the midpoint of the opposite side. |

Triangle Midsegment Theorem | A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. |

indirect proof | Begin by assuming that the conclusion is false. Then show that this assumption leads to a contradiction. Also known as a "proof by contradiction". |

Angle-Side Relationships in Triangles - Theorem 1 | If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. |

Angle-Side Relationships in Triangles - Theorem 2 | If two angles of a triangle are not congruent, then the longer side is opposite the larger angle. |

Triangle Inequality Theorem | The sum of any two side lengths of a triangle is greater than the third side length. |

Pythagorean Theorem | In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. |

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

Pythagorean Inequalities Theorem | In ∆ABC , 'c' is the longest side. If c² > a² + b², the ∆ABC is an obtuse triangle. If c² < a² + b², then ∆ABC is an acute triangle. |

45°-45°-90° Triangle Theorem | In a 45°-45°-90° triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times √2. |

30°-60°-90° Triangle Theorem | In a 30°-60°-90° triangle, the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is the length of the shorter leg times √3. |

Created by:
cawhite