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# Geometry Terms

TermDefinition
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
Created by: lyndseyjeffries

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