geometry-definitions.txt

 Biconditional p if and only if q," single statement that is equivalent to writing the conditional statement and its converse Conclusion The part of the conditional statement that follows the word "then." (Notation is q) Conditional Statement Has the form "If p, then q." p is the hypothesis and q is the conclusion Conjecture A conclusion reached by inductive reasoning Contrapositive Formed by interchanging and negating the hypothesis and conclusion "If not q, then not p" Converse Formed by interchanging the hypothesis and conclusion "If q, then p" Counterexample An example of a conditional statement in which the hypothesis is fulfilled and the conclusion is not fulfilled. Proves that the statement is false Deductive Reasoning Using the laws of logic to prove statements (theorems) from known statements (postulates and previously proved theorems) Equivalent Statements Having the same truth value Hypothesis In a conditional statement, it comes after "if"...the p in "if p, then q." Inductive Reasoning Making a conjecture about several examples after looking for a pattern in the examples Intuitive Reasoning Using your feelings Inverse Negating the hypothesis and conclusion "If not p, then not q" Law of Detachment If "If p, then q" is a true conditional statement and p is true, then q is true Law of Syllogism If "If p, then q" and "If q, then r" are true conditional statements, then "If p, then r" is also true Negation The denial of a statement "Not p" Truth Value naming a statement true or false Transformation Movement of a pre-image using reflection translation rotation or dilation Reflection Isometric flip motion Rotation Isometric turn motion Translation Isometric slide motion Dilation A similarity transformation that has a center and scale factor, can be an enlargement or a reduction Pre-image Original object before a transformation Image The object after a transformation Congruent Same size and shape Isometry Congruent transformation Angle of Rotation The angle at which a figure is rotated Center of Dilation Point about which a dilation is performed Center of Rotation Fixed point around which a rotation occurs Equidistant Same or equal distance Line of Reflection For every point on a figure, there is a reflection image of that point over this line Prime Notation Symbolic representation given to images as a result of a transformation Similarity Transformation Dilation Symmetry A figure has this if there is an isometry that maps the figure onto itself Corresponding Matching parts of two or more figures on another figure ... Mapping A one-to-one correspondence between points of two figures Scale Factor The number that describes the size change from an original figure to its image ... Composition of Motions Two or more motions done in sequence Matrix A collection of data using rows and columns Dimensions of Matrix Row by Column Identity Matrix Matrix when used results in the original matrix e11 = 1 e12 = 0 e21 =0 e22 = 1 Acute Angle An angle x whose measure is 0 < x< 90 Adjacent Angles A pair of angles that: 1)Share a common vertex Analytic Geometry Coordinate based geometry Angle A partial rotation Angle Bisector A ray, line, or plane that divides an angle into two congruent angles Bisect Divided into two equal or congruent parts Collinear On the same line Complementary Angles A pair of angles whose sum is 90 degrees Congruent Angles Angles that have the same measure Congruent Segments Segments that have the same length Coplanar On the same plane Degree Unit of measure for an angle (1/360th of a full rotation) Dihedral Angle Angle formed by the intersection of two planes Endpoint Point at the beginning or end of a ray or segment Euclidean Geometry Non-coordinate geometry Exterior Point A point not in the interior or on Finite Having a limit Geometry (overall) The mathematics of the properties measurement and relationships of points lines angles surfaces and solids Infinite Having no limits or boundaries in time or space or extent or magnitude Interior Point A point not in the exterior or on Intersection Set of points shared by two or more figures Line Infinite set of collinear points Linear Pair A pair of adjacent angles whose non-adjacent sides form opposite rays Midpoint A point that divides a segment into two congruent segments Non-collinear Not on the same line Obtuse Angle An angle q whose measure is 90 < q < 180 Opposite Rays Two rays that share a common endpoint and extend in opposite directions Parallel Lines Coplanar lines that never intersect Parallel Planes Two or more planes that never intersect Perpendicular Bisector A segment bisector that intersects the midpoint at right angle Perpendicular Lines Two lines that intersect to form one right angle Plane A boundless flat surface Plane Geometry Branch of geometry that deals with geometric figures which require a plane but not any space for their existence Point Undefined, but can be described as an exact unique sizeless location in space Postulate A statement that requires no proof Ray Has an endpoint and extends infinitely in 1 direction Right Angle An angle q whose measure is q = 90 Segment An infinite set of collinear points with finite length Segment Bisector A line, segment, ray, or plane that intersects a midpoint of a segment Skew Lines Non-coplanar lines that never intersect Solid Geometry Branch of geometry that deals with figures which occupy space Space Infinite set of all points everywhere Straight Angle An angle q whose measure is q = 180 Supplementary Angles A pair of angles whose sum is 180 Theorem A statement that requires proof Three-Dimensional Figure A geometric figure that takes up space in solid geometry like a pyramid or sphere Trisect Divide into three equal or congruent parts Two-Dimensional Figure A geometric figure that takes up no space and can be represented in a plane like a triangle or circle Vertex The shared endpoint of two rays that form an angle Vertical Angles A pair of angles whose sides form opposite rays Alternate Exterior Angles Angles that lie outside two lines on opposite sides of the transversal Alternate Interior Angles Angles that lie between two lines on opposite sides of the transversal Consecutive Interior Angles (Same-Side Interior) Two angles that lie between two lines on the same side of the transversal Corresponding Angles Angles that occupy corresponding positions Point-Slope Form - (y - y1) = m(x - x1) ... Transversal A line that intersects two or more coplanar lines at different points Slope (y2 - y1)/(x2 - x1) Standard Form For linear equations, the form Ax + By = C, where A,B,C are integers and A doesn't equal 0 Slope-Intercept Form A linear equation of the form y = mx + b AuthorAnonymous ID127070 Card Setgeometry-definitions.txt DescriptionHonors Geometry vocabulary terms Updated2012-01-11T01:28:57Z Show Answers