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# Geometry

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

Altitude of a triangle | A straight line through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side) of a triangle |

Angle bisector theorem | Concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle. |

Arc | A closed segment (symbol: ⌒) of a differentiable curve in the two-dimensional plane |

Area | Any particular extent of space or surface. A=L*W (Always write area in #measure squared). |

Center of a polygon | In a rotation, the point that does not move. The rest of the plane rotates around this one fixed point. |

Centroid of a triangle | The point where the three medians of the triangle intersect |

Circumcenter of a triangle | The point where the three perpendicular bisectors of a triangle meet |

Circumference (circles) | A complete circular arc; also the distance around the outside of a circle. C=Pi*r(r). |

Circumscribed | A geometric figure that is drawn around another geometric figure so as to touch all its vertices |

Combination | A way of selecting several things out of a larger group, where (unlike permutations) order does not matter. |

Compass | An instrument for drawing circles and arcs and measuring distances between points, consisting of two arms linked by a movable joint. |

Composition | The combining of distinct parts or elements to form a whole |

Compound event | An event whose probability of occurrence depends upon the probability of occurrence of two or more independent events |

Compression | To reduce a shape in size while retaining proportions |

Conditional probability | The probability that an event will occur, when another event is known to occur or to have occurred |

Conditional probability formula | The conditional probability of A given B is denoted by P(A|B) and defined by the formula P(A|B) = P(AB) P(B), provided P(B) > 0. |

Dependent events | When the outcome of one event affects the outcome of another. |

Dilation | A transformation that grows or shrinks a polygon by a given proportion about a center point |

Events | A set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned |

Experimental probability | The ratio of the number of times the event occurs to the total number of trials |

Frequency table | Lists items and uses tally marks to record and show the number of times they occur |

Fundamental counting principle | When there are m ways to do one thing, and n ways to do another, then there are m×n ways of doing both. |

Glide reflection | A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation |

Glide reflectional symmetry | The symmetry that a figure has if it can be made to fit exactly onto the original when it is translated a given distance at a given direction and then reflected over a line. |

Hypotenuse-leg theorem (HL theorem) | If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. |

Image | An optically formed duplicate, counterpart, or other representative reproduction of an object, especially an optical reproduction formed by a lens or mirror |

Incenter of a triangle | The point where the three angle bisectors of a triangle meet |

Included angle | The angle made by two lines with a common vertex |

Independent events | When the outcome of one event does not influence the outcome of thesecond event |

Inscribed in (the triangle) | Drawing one shape inside a triangle so that it just touches the sides of the triangle |

Intersection | The probability that events A and B both will occur |

Isometry | A transformation that is invariant with respect to distance. That is, the distance between any two points in the pre-image must be the same as the distance between the images of the two points. |

Median of a triangle | A line segment joining a vertex of a triangle to the midpoint of the opposing side |

Midsegment of a triangle | The segment joining the midpoints of two sides of a triangle |

Mutually exclusive events | Two events that cannot occur at the same time |

n factorial | The factorial of a natural number n is the product of the positive integers less than or equal to n. |

Non-included angle | The side of a triangle that is not included by two given angles |

Ordered triple | Three numbers written in the form (x, y, z) |

n-tuple | n numbers written in the form (x1, x2, x3, . . . , xn) |

Orthocenter of a triangle | The point where the three altitudes of a triangle intersect |

Overlap | Similar triangles in which one triangle is on top of (overlapping) another triangle |

Permutation | All possible arrangements of a collection of things, where the order is important |

Point of symmetry | A special center point for certain kinds of symmetric figures or graphs. If a figure or graph can be rotated 180° about a point P and end up looking identical to the original, then P is a point of symmetry. |

Polygon angle-sum theorem, corollary | The measure of each interior angle of a regular n-gon is 180*(n–2)/n) |

Polygon exterior angle-sum theorem | If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360. |

Preimage | The original figure prior to a transformation. |

Probability distribution | A graph, table, or formula that gives the probability for each value of the random variable |

Probability formula | The number of ways an event can occur divided by the total number of possible outcomes |

Relative frequency | The ratio of the actual number of favorable events to the total possible |

Remote interior angles | The two angles of a triangle that are not adjacent to the exterior angle, which is drawn by extending one of the sides. |

Rigid motion | The variance in position and orientation when a rigid body moves |

Sample space | In probability theory, the set of all possible outcomes or results of an experiment |

Tessellation | A plane with identically shaped pieces that do not overlap or leave blank spaces. The pieces do not have to be oriented identically. A tessellation may use tiles of one, two, three, or any finite number of shapes. |

Theoretical probability | The likelihood of an event happening based on all the possible outcomes |

Transformation | Operations that alter the form of a figure. The standard transformations are translations, reflections, dilations (stretches), compressions (contractions or shrinks), and rotations. |

Tree diagram | A representation of a tree structure in which the probability of each branch is written on the branch and the outcome is written at the end of the branch |

Volume (prisms, cylinders, pyramids, cones, spheres) | The total amount of space enclosed in a solid. (Always write volume in #measure cubed). |