Geometry final honors

Point One of the undefined terms in geometry. A point is a location. It has neither size nor shape.
Line One of the undefined terms in geometry. A line is made up of points and has no thickness or width.
Plane One of the undefined terms in geometry. A plane is a flat surface made up of points that has no depth and extends indefinitely in all directions.
Collinear points Points that lie on the same line.
Noncollinear points Points that do not lie on the same line.
Coplanar points Points that lie in the same plane.
Noncoplanar points Points that do not lie in the same plane.
Intersection The intersection of two or more geometric figures is the set of points they have in common.
Definitions (defined term) Explained using undefined terms and/or other defined terms.
Space A boundless, three-dimensional set of all points.
Locus The set of points that satisfy a particular condition.
Line segment (segment) A measurable part of a line that consists of two points, called endpoints, and all of the points between them.
Betweenness of points (between) For any two points A and B on a line, there is another point C between A and B if and only if A, B, and C are collinear and AC + CB = AB.
Congruent segments Segments that have the same measure are congruent segments.
Congruent Having the same measure.
Construction Methods of creating figures without the benefit of measuring tools. Generally, only a pencil, straightedge, and compass are used.
Distance The distance between two points is the length of the segment with those points as its endpoints.
Irrational number A number that cannot be expressed as a terminating or repeating decimal.
Midpoint The midpoint of a segment is the point halfway between the endpoints of the segment.
Segment bisector Any segment, line or plane that intersects a segment at its midpoint is a segment bisector.
Ray A part of a line: it has one end point and extends indefinitely in one direction.
Opposite rays Two collinear rays with a common endpoint.
Angle An angle is formed by two noncollinear rays that have a common endpoint. The rays are called SIDES and the common endpoint is called the VERTEX.
Interior A 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.
Exterior A point is in the exterior of an angle if it is neither on the angle nor in the interior of the angle.
Inductive reasoning Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction.
Conjecture An educated guess based on known information.
Counterexample An example used to show that a given statement is not always true.
Statement Any sentence that is either true or false, but not both.
Truth value The truth or falsity of a statement.
Negation If a statement is represented by p, then not p is the negation of the statement.
Compound statement A statement formed by joining two or more statements.
Conjunction A compound statement formed by joining two or more statements with the word and.
Disjunction A compound statement formed by joining two or more statements with the word or.
Truth table A table used as a convenient method for organizing the truth values of statements.
Conditional statement A statement that can be written in 'if-then' form.
If-then statement A compound statement of the form 'if p, then q' where p and q are statements.
Hypothesis In a conditional statement, the statement that immediately follows the word 'if'.
Conclusion In a conditional statement, the statement that immediately follows the word 'then'.
Related conditionals Statements that are based on a given conditional statement.
Converse The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
Inverse The statement formed by negating both the hypothesis and conclusion of a conditional statement.
Contrapositive The statement formed by negating both the hypothesis and the conclusion of the converse of a conditional statement.
Logically equivalent Statements that have the same truth values.
Deductive reasoning A system of reasoning that uses facts, rules, definitions or properties to reach logical conclusions.
Valid Logically correct.
Law of Detachment If p → q is a true conditional, and p is true, then q is also true.
Law of Syllogism If p → q and q → r are true conditionals, then p → r is also true.
Postulate (also known as axiom) A statement that describes a fundamental relationship between the basic terms of geometry. Postulates are accepted as true without proof.
Proof A logical argument in which each statement you make is supported by a statement that is true.
Theorem A statement of conjecture that can be proven true by using undefined terms, definitions and postulates.
Deductive argument A proof formed by a group of algebraic steps used to solve a problem.
Algebraic proof A proof that is made up of a series of algebraic statements. The properties of equality provide justification for many statements in algebraic proofs.
Two-column proof A formal proof that contains statements and reasons.
Parallel lines Coplanar lines that do not intersect.
Skew lines Lines that do not intersect and are not coplanar.
Parallel planes Planes that do not intersect.
Transversal A line that intersects two or more coplanar lines at two different points.
Interior angles Angles that lie between two lines that intersect the same transversal.
Exterior angles Angles that lie in the region that is not between two lines that intersect the same transversal.
Consecutive interior angles Interior angles that lie on the same side of the transversal.
Alternate interior angles Nonadjacent interior angles that lie on opposite sides of the transversal.
Alternate exterior angles Nonadjacent exterior angles that lie on opposite sides of the transversal.
Corresponding angles Angles that lie on the same side of the transversal and the same side of the two lines cut by the transversal.
Slope of a line The ratio of the change along the y-axis to the change along the x-axis between any two points on the line.
Rate of Change Another name for slope.
Slope-intercept form of a linear equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Point-slope form of a linear equation y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope of the line.
Equidistant The distance between two lines measured along a perpendicular line is always the same.
Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.
Two nonvertical lines have the same slope If and only if they are parallel. All vertical lines are parallel.
Two nonvertical lines are perpendicular If and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
Converse of Corresponding Angles Postulate If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
If given line and a point not on the line Then there exists exactly one line through the point that is parallel to the given line.
Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent.
Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary.
Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent.
Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Alternate Exterior Angles Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Consecutive Interior Angles Converse If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are parallel.
Two lines Equidistant from a Third In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.
Acute Triangle A triangle in which all of the angles are acute angles.
Equiangular Triangle A triangle with all angles congruent.
Obtuse Triangle A triangle with an obtuse angle.
Right Triangle A triangle with a right angle.
Hypotenuse The side opposite the right angle in a right triangle.
Legs (of a right triangle) The other two sides of a right triangle.
Equilateral Triangle A triangle with all sides congruent.
Isosceles Triangle A triangle with at least two sides congruent.
Scalene Triangle A triangle with no two sides congruent.
Auxiliary line An extra line or segment drawn in a figure to help analyze geometric relationships.
Remote Interior Angles In a polygon, angles that are not adjacent to the given exterior angle.
Corollary A theorem with a proof that follows as a direct result of another theorem.
Congruent Polygons Two polygons are congruent if and only if their corresponding parts are congruent.
Included Angle The angle formed by two adjacent sides of a polygon.
Included Side The side located between two consecutive angles of a polygon.
Median The median of a triangle is a segment with endpoints of a vertex of the triangle and the midpoint of the opposite side.
Altitude The altitude of a triangle is a segment from a vertex to the line containing the opposite side, and perpendicular to the line containing that side.
Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180.
Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent.
Reflexive Property of Triangle Congruence ΔABC ≅ ΔABC
Symmetric Property of Triangle Congruence If ΔABC ≅ ΔEFG, then ΔEFG ≅ ΔABC
Transitive Property of Triangle Congruence If ΔABC ≅ ΔEFG and ΔEFG ≅ ΔJKL, then ΔABC ≅ ΔJKL
Angle-Angle-Side (AAS) Congruence If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
Side-Angle-Side (SAS) Congruence If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
Angle-Side-Angle (ASA) Congruence If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Hinge Theorem If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Hinge Converse If two sides of a triangle are congruent to two sides of another triangle, and the third side in the first is longer than the third side in the second triangle, then the included angle measure of the first triangle is greater than the included angle measure in the second triangle.