Semester 1 Finals Vocabulary – Flashcards
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Undefined term
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Words that are not formally explained by means of more basic words/concepts- point, lines, plane
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Point
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Basic undefined term in geometry. Point is a location, representedby a dot, and named by capital letters
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Line
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Basic undefined term in geometry. Made up of points, no thickness or width, shown with an arrowhead at each end, etc.
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Plane
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Basic undefined term in geometry. Flat surface madeup of points that has no depth and extends infinitly in all directions.
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Collinear
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Points that lie on the same line
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Coplanar
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Points that lie on the same plane
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Intersection
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Set of points common rto two or geometric figures
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Definition/ Defined term
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Term that is explaines using undefined terms and or other defined terms
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Space
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Boundless three-dimensional set of all points
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Line segment
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Measurable part of a line that consists of 2 points called endpoints ans all points between them
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Between/Betweenness of points
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For any 2 points A and B on a line there is another point C betwern A and B if and only if A, B, and C are collinear and AC+ CB= AB
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Congruent segments
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Segments that have the same measure
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Construction
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Method of creating geometric figure without brnefit of measuring tools
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Distance
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Length if the segment btwn 2 points
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Irrational number
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A number that cannor be expressed as a terminating or repeating decimal
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Midpoint
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Point on a segment excatly halfway between the endpoints of the segments
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Segment bisector
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Segment/line/plane that intersects a segment at its midpoint
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Ray
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PQ is a ray if it is set of points consiting of PQ and all points S for which Q is between P and S
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Opposite Rays
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2 rays BA and BC such that B is btwn A and C
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Angle
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Intersection of 2 noncollinear rays at a common endpoint
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Side
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Ray of an angle
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Vertex
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Common endpoint of 2 segment or rays
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Interior
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Point is in the interior of an angle if it does not lie on the angle itself and it lies on a segment with endpoints that are on the sides of the angle
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Exterior
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A point in the exterior of an angle if it is neither on the angle nor in the interior of the angle
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Degree
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A unit of measure used in measuring angles and arcs
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Right angles
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90*
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Acute
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Less than 90
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Obtuse
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More than 90
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Angle bisector
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A ray that divides an angle into 2 congruent angles
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Adjacent angles
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2 angles that lie in the same plane, have a common vertex, and a common side but no common interior points
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Linear pair
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A pair of adjacent angles whose noncommon side are opposite rays
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Vertical angles
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Two nonadjacent angles formed by 2 intersecting lines
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Complementary angles
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2 angles with measures that have the sum of 90
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Supplementary angles
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Two angles with measure that have the sum 180
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Perpendicular
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Lines that form right angles
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Inductive reasoning
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Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction.
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Conjecture
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An educated guess based on known information
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Counterexample
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An example usero show that a given statement is not always true
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Statement
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Any sentence that is either true or false but not both
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Truth value
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The true or falsity of a statement
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Negation
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If a statement is represented by p and then not p is rhe negation of the statement
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Compound statement
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A statement formed by joining two or more statement
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Conjunction
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A compound statement formed by joing two or more statements with the word and
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Disjunction
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Compound statement formed by joining two or more statement with the word or
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Truth table
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A title used as a convenient method for organizing truth values of statements
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Conditional statement
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A statement that can be written in if-then form
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If then statement
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A compound statement of the form if p then q where p and q are statements
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Hypothesis
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In a conditional stament, he statement that immediatelyfollows the word if
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Conclusion
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In a conditional statement, the statement that immediately follows the word then
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Related conditionals
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Statements that are based on a given conditional statement
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Converse
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Statement formed by exchanging the hypothesis and conclusion of a conditional statement
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Inverse
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Statement formed by negating both hypothesis and conclusion of a conditional statement
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Contrapositive
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Statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement
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Logically equivalent
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Statements that have the same truth values
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Deductive Reasoning
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System of reasoning that uses facts, rules, definitions, or properties to reach logical conclusion
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Valid
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To my logically correct
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Postulate
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Statement that describes a fundamental relationship btwn the basic terms of geo
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Axiom
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Statement that is a accepted as true
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Proof
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Logical arguement in which each staement you make is supported by a statement that is accepted as true
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Theorem
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Statment or conjecture that can be proven true by undefined terms, defs, and potulates
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Deductive argument
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Proof formed by a group of algebraic steps used to solve a problem
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Paragraph proof
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Informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true
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Algebraic proof
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Proof made up of a series of algeb raic statments
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2 column proof
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Step- statement Reasons- properies that justify each step
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Formal proof
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2 column proof containing statements and reasons
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Parallel lines
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Coplanar lines that do not intersect
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Skew lines
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No coplanr and do not intersect
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Parallel planes
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Planes do not intersect
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Transversal
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Line that intersect two or more lines in a plane at different points
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Interior angles
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Angles that lie btwn 2 transversals that intersect the same line
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Exterior angles
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Angle that lies in the region that is not btwn 2 transversals that intersect the same line
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Slope
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y2-y1/x2-x1
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Rate of change
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Describes how a quantity is changing over time
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Slope intercept form
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y=mx+b
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Equidistant
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The distannce btwn 2 lines measured along a perpendicular line is always the same
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Equiangular triangle
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A triangle with all angles congruent
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Equilateral triangle
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All sides congruent
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Scalene triangle
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No 2 sides congruent
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Auxiliary line
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Extra line or segment drawn in a figure to help complete a proof
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Remote interior
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Angles of a triangle that are not adjacent to a given exterior angle
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Corollary
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Statement that can be easily proved using a theorem is called a collary of that theorem
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Congruent
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Having same measure
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Congruent polygons
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Polygons in which all matching parts are congruen
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Corresponding parts
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Matching parts of congruent polygons
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Included angle
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Angle formed by 2 sides is the included angle for those 2 sides
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Vertex angle
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Angle formed by the intersection of 2 sides of a polygon
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Base angles
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2 angles formed by the base and the congruent sidesof an isosceles triangle
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Transformation
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In a plane for which each poinr has exactly one image point and each image point has exactly one preimage point
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Preimage
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Graph of an object before transformation
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Image
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Figure that results from the transformation of a geometric figure
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Congruence transformation
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Mapping for which a geometric figure and its image are congruent
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Isometry
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Mapping for which original figure and its image are congruent
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Coordinate proof
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Proof that uses figures in the coordinate plane Ns algebra to prove a geometric concept
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Perpendicular bisector
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Line segment or ray that passes through the mdpt of a side and is perpendicular to that side
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Concurrent lines
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3 or more lines that intersect at a common point
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Point of concurrency
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Point of intersection of concurrent lines
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Circumcenter
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Point of concurrency of perpendicular bisectors of a triangle
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Incenter
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Point of concurrency of of the angle bisectors of a triangle
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Median
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In a triangle a line segment with endpoints thar are a vertex of a triangle and the midpoint of the side opposite the vertex
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Centroid
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Point of concurrency of the medians of a triangle
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Orthocenter
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Point of concurrency of the altitudes of a triangle
