Normal Size Small Size show me how
|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.
|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
|A complete circular arc; also the distance around the outside of a circle
|A geometric figure that is drawn around another geometric figure so as to touch all its vertices
|A way of selecting several things out of a larger group, where (unlike permutations) order does not matter.
|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
|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)
|An event whose probability of occurrence depends upon the probability of occurrence of two or more independent events
|To reduce a shape in size while retaining proportions
|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.
|The drawing of various shapes using only a compass and straightedge or ruler. No measurement of lengths or angles is allowed.
|When the outcome of one event affects the outcome of another (see also independent events, mutually exclusive events)
|Either of two points marking the end of a line segment (see also midpoint)
|A set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned
|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)
|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.
|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)
|An optically formed duplicate, counterpart, or other representative reproduction of an object, especially an optical reproduction formed by a lens or mirror
|The angle made by two lines with a common vertex
|When the outcome of one event does not influence the outcome of the second event (see also dependent events, mutually exclusive events)
|Any of the four angles formed between two straight lines intersected by a third straight line (see also exterior angle)
|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)
|The factorial of a natural number n is the product of the positive integers less than or equal to n.
|The side of a triangle that is not included by two given angles
|Three numbers written in the form (x, y, z) (see also ordered pair, 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
|The result of an experiment in probability theory
|Similar triangles in which one triangle is on top of (overlapping) another triangle
|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.
|The original figure prior to a transformation.
|A graph, table, or formula that gives the probability for each value of the random variable
|The number of ways an event can occur divided by the total number of possible outcomes (see also conditional probability formula)
|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.
|A part of a line that begins at a particular point (called the endpoint) and extends endlessly in one direction
|A transformation that creates a mirror image of a shape (see also glide reflection).
|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
|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 The variance in position and orientation when a rigid body moves
|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.
|In probability theory, the set of all possible outcomes or results of an experiment
|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.
|The tangent of the angle between a given straight line and the x-axis of a system of Cartesian coordinates
|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
|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)
|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.
|The likelihood of an event happening based on all the possible outcomes (see also complement probability, conditional probability, experimental probability, probability)
|Operations that alter the form of a figure. The standard transformations are translations, reflections, dilations (stretches), compressions (contractions or shrinks), and rotations.
|A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation
|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