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# Geometry Terms

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

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 |

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 |

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. |

Common parts | Informal language that describes similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length) of two- and three-dimensional shapes, in different sizes and orientations |

Complement probability | In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. (see also conditional probability, experimental probability, probability, theoretical probability) |

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 (see also complement probability, experimental probability, probability, theoretical probability) |

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. (see also probability formula) |

Congruency by AAS, ASA, SAS, SSS | Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. |

Construction | The drawing of various shapes using only a compass and straightedge or ruler. No measurement of lengths or angles is allowed. |

Dependent events | When the outcome of one event affects the outcome of another (see also independent events, mutually exclusive events) |

Endpoint | Either of two points marking the end of a line segment (see also midpoint) |

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 (see also complement probability, conditional probability, probability, theoretical probability) |

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 (see also reflection). |

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. (see also reflectional symmetry, rotational symmetry, symmetry) |

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

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 the second event (see also dependent events, mutually exclusive events) |

Interior angle | Any of the four angles formed between two straight lines intersected by a third straight line (see also exterior angle) |

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. |

Isosceles triangle theorem, converse | If two angles of an isosceles triangle are congruent, the sides opposite them are congruent. |

Line of symmetry | The line of symmetry of a two-dimensional figure is a line such that, for each perpendicular constructed, if the perpendicular intersects the figure at a distance d from the axis along the perpendicular, then there exists another intersection of the figur |

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

Midpoint formula in the coordinate plane | The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. |

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 (see also dependent events, independent events) |

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) (see also ordered pair, n-tuple) |

n-tuple | n numbers written in the form (x1, x2, x3, . . . , xn) (see also ordered pair, ordered triple) |

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

Outcome | The result of an experiment in probability theory |

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 |

Perpendicular bisector theorem | The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. |

Perpendicular bisector theorem, converse | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |

Point of concurrency | The point where three or more lines intersect |

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. (see also line of symmetry) |

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 (see also conditional probability formula) |

Pythagorean theorem | An equation relating the lengths of the sides of a right triangle. The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. The formula is a2 + b2 = c2. |

Ray | A part of a line that begins at a particular point (called the endpoint) and extends endlessly in one direction |

Reflection | A transformation that creates a mirror image of a shape (see also glide reflection). |

Reflectional symmetry | The descriptive term for an object or figure that is indistinguishable from its transformed image (see also glide reflectional symmetry, rotational symmetry, symmetry) |

Reflexive property of equality | Anything is equal to itself |

Relative frequency | The ratio of the actual number of favorable events to the total possible number of events; often taken as an estimate of probability |

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

Rotational symmetry | When an object that looks the same after a certain amount of rotation (see also glide reflectional symmetry, reflectional symmetry, symmetry) |

Same-side exterior angles | Exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles is outside the parallel lines, and on the same side of the transversal. |

Same-side interior angles | When two parallel lines are intersected by a transversal, one type of angle formed is same-side interior angles. Same side interior angles are pairs of angles that are found on the same side of the transversal. |

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

Segments | A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points. |

Slope | The tangent of the angle between a given straight line and the x-axis of a system of Cartesian coordinates |

Straightedge | A bar or piece of material (wood, metal, plastic, etc) with a straight edge for testing straight lines and surfaces or for cutting along or drawing straight lines |

Symmetry | Illustrated by a geometric figure or a graph consisting of two parts that are congruent to each other (see also glide reflectional symmetry, reflectional symmetry, rotational symmetry) |

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 (see also complement probability, conditional probability, experimental probability, probability) |

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

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

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 |