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# Math Mid Term

Term | Definition |
---|---|

Point | One place in space, has no dimensions. |

Line | Has one dimension, is represented by a line with two arrowheads but extends infinitely in both directions. Through any two points there is exactly one line. |

Plane | has two dimensions, it extends without end in both directions. through any three points that are not all on the same line there is on plane. |

Collinear Points | points that lie on the same line. |

Coplanar Points | points that lie in the same plane. |

Segment | a section of a line that has two endpoints and includes only points between the two endpoints. |

Ray | has one endpoint and extends infinitely in one direction. Named by the endpoint and a point collinear to the endpoint. Includes all points on the same side of the endpoint as the other point. |

Opposite Rays | Rays that extend infinitely in opposite directions but share a common point. |

Intersection | the common point(s) that two figures share. |

Postulate | A rule that is accepted without proof. |

Theorem: A rule that is proven. | A rule that is proven. |

Ruler Postulate | The distance between points is the difference between the two. |

Segment Addition Postulate | If a point is between two other points, segment AB+BC=AC |

Midpoint | The point that divides the segment into two congruent segments. |

Segment Bisector | a line that intersects a line at its midpoint. |

Angle | Two rays with the same endpoint. The rays make up the sides and the endpoint is the vertex. |

Acute Angle | measures less than 90 degrees |

Right Angle | measures 90 degrees |

Obtuse Angle | measures more than 90 degrees |

Straight Angle | measures 180 degrees |

Protractor postulate | The measure of an angle is the difference between the two sides. |

Angle Addition Postulate | If there is an extra ray inside an angle the measure of the two mini angles made by the extra ray add together to get the overall angle. So L ABD + L DBC = LABC. |

Angle Bisector | A ray that divides an angle into two angles that are equal in measure. |

Complementary Angles | Two angles whose measures sum to 90 degrees. |

Supplementary Angles | Two angles whose measures sum to 180 degrees. |

Adjacent Angles | Two angles that share a common side and vertex. |

Linear Pair | Supplementary adjacent angles whose noncommon sides are opposite rays |

Vertical Angles | Share a common vertex, and have sides that make two pairs of opposite rays. |

Polygon | A closed figure formed by three or more line segments called sides. Each endpoint of a side is called a vertex. |

Convex Polygon | All sides if extended do not go inside of the polygon. |

Concave Polygon | One or more sides of a shape if extended go inside of the polygon. |

Equilateral Polygon | All sides are congruent. |

Equiangular Polygon | All interior angles are congruent. |

Regular Polygon | A convex equilateral equiangular polygon. |

Parallel lines | Don’t intersect and are coplanar. |

Skew Lines | Don’t intersect and are not coplanar. |

Parallel Postulate | If there is a line and a point not on the line there is exactly one line through the point that is parallel to the line. |

Perpendicular Postulate | If there is a line and a point not on the line then there is exactly one line through the point that is perpendicular to the line. |

Transversal | The line that intersects two or more coplanar lines at different points. |

Corresponding Angles | Angles in a transversal that have corresponding positions. |

Alternate Interior Angles | Angles in a transversal that lie between two lines on opposite sides of the transversal |

Alternate Exterior Angles | Angles in a transversal that lie outside the lines on opposite sides of the transversal. |

Consecutive Interior Angles | Angles in a transversal that lie between the two lines on the the same side of the transversal. |

Corresponding Angles Postulate | If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent. |

Alternate Interior Angles Theorem | If two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent. |

Alternate Exterior Angles Theorem | If two parallel lines are cut by a transversal then the pairs of alternate exterior angles are congruence |

Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal the pairs of consecutive interior angles are supplementary.. |

Corresponding Angles Converse Postulate | If two lines are cut by a transversal so that the pairs of corresponding angles are congruent the lines are parallel. |

Alternate Interior Angles Converse Theorem | If two lines are cut by a transversal so that the pairs of alternate interior angles are congruent then the lines are parallel. |

Consecutive Interior angles Theorem | If two lines are cut by a transversal so the consecutive interior angles are supplementary then the two lines are parallel. |

Transitive Property of Parallel Lines | If two lines are parallel to the same line they are parallel to each other. |

Slopes of Parallel Lines Postulate | If two lines are parallel then they have the same slope. |

Slopes of Perpendicular Lines | If two lines are parallel then their slopes product is - 1 . |

Perpendicular Transversal Theorem | If a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other. |

Lines Perpendicular To A Transversal Theorem | In a plane if two lines are perpendicular to the same line then they are parallel to each other. |

Conjecture | An unproven statement that is based on reason. |

Inductive Reasoning: Uses patterns and observations to prove a conjecture true. | |

Counterexample: A case which proves a conjecture false. | |

Conditional Statement: A logical statement that has two parts a hypothesis and conclusion written in if then form so the hypothesis is the if and the conclusion is the then. | |

Converse: The original conditional statement is switched so that the original hypothesis is switched with the original conclusion. | |

Inverse: The original conditional statement is switched so that is original hypothesis and conclusion are opposite but in the same order. | |

Contrapositive: The inverse of the converse of the original statement. | |

Perpendicular: Two lines that intersect to form a 90 degree angle. | |

Biconditional Statement: Both the original statement and its converse are true so they can be written as a single if and only if statement. | |

Deductive Reasoning: Uses facts to form a logical argument to prove a conjecture true. | |

Law of detachment: If the hypothesis of a statement is true then the conclusion is also true. | |

Law of Syllogism: If the then of one statement is the if of another then the if of the first can be combined with the then of another to make a new statement. | |

Through any two points there is one | line |

A line contains at least | two points |

If two lines intersect they intersect at | one point. |

Through any three non collinear points there is | one plane. |

A plane contains at least | three points |

If two points lie in a plane | then the line containing them lies in the plane. |

If two planes intersect | then their intersection is a line. |

Addition Property | If you add a number to one side of an equation you must add it to the other. |

Subtraction Property | If you subtract a number from one side you must subtract it from the other. |

Multiplication Property | If you multiply on one side you must multiply on the other side. |

Division Property | If you divide on one side you must divide on the other. |

Substitution | If two numbers are equal one can be substituted for the other in any equation. |

Distributive Property | If numbers are in parentheses you must distribute all numbers outside parentheses to all numbers inside. |

Reflexive Property | Anything is equal to itself. |

Symmetric Property | Any equation can be reversed |

Transitive Property | If A=B and B=C A=C |

Proof | A logical argument that shows a statement is true. |

Two Column Proof | Has numbered statements that correspond with reasons thats how an argument in logical order. |

Theorem | A statement that can be proven. |

Congruent Supplements Theorem | If two angles are supplementary to the same angle they are congruent. |

Congruent Complements Theorem | If two angles are complementary to the same angle then they are congruent. |

Linear Pair Postulate | If two angles form a linear pair then they are supplementary. |

Vertical Angles Congruence Theorem | Vertical angles are congruent. |

Triangle Sum Theorem | The sum of a triangles interior angles is 180˚ |

Exterior Angle Sum Theorem | The measure of an exterior angle is equal to the sum of the two opposite interior angles. |

Corollary To The Triangle Sum Theorem | The acute angles of a right triangle are complementary. |

Third angles Theorem | If two angles of one triangle are congruent to two pairs of angles of another triangle, then the third angles are also congruent. |

SSS Postulate | If three sides of a triangle are congruent to three sides of a second triangle then the triangles are congruent. |

SAS Postulate | If Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent. |

HL Theorem | If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle then the triangles are congruent. |

ASA Postulate | If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the triangles are congruent. |

AAS Theorem | If two angles and the non included side of one triangle are congruent to two angles and the non included side of a second triangle then the two triangles are congruent to one another. |

CPCTC: | Corresponding parts of congruent triangles are congruent. |

Base Angles Theorem | If two sides of a triangle are congruent then the angles opposite them are congruent. |

Converse of The Base Angles Theorem | If two angles of a triangle are congruent then the sides opposite them are congruent. |

Midsegment | The segment that runs from the midpoint of one side to the midpoint of the other. |

Coordinate Proof | Prof things about figures using coordinates, or using figures prof things about coordinates. |

Midsegment Theorem | A midsegment is half of the third side and parallel to the third side. |

Concurrent | When 3 or more lines intersect at the same point |

Point of Concurrency | The point where 3 or more lines intersect. |

Equidistant | a point that is the same distance between two figures. |

Perpendicular Bisector | A line that is at the midpoint of a segment and is perpendicular to the segment. |

Circumcenter | The point where three perpendicular bisectors meet. |

Perpendicular Bisector Theorem | If a point is on the perpendicular bisector it is equidistant from the endpoint of the segment. |

Converse of The Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment then it is on the perpendicular bisector. |

Concurrency of Perpendicular Bisectors of A Triangle Theorem | The perpendicular bisectors of a triangle intersect at a point that is equidistant from all vertices. |

Incenter | The point of concurrency of the angle bisectors of a triangle. |

Angle Bisector Theorem | If a point is on the angle bisector it is equidistant from the two sides of an angle if the segment measured is perpendicular. |

Converse of The Angle Bisector Theorem | If a point inside an angle is equidistant from the sides of the angle it is on the angle bisector but only if the segment measured is perpendicular. |

Concurrency of Angle Bisectors of a Triangle Theorem | The angle bisectors of a triangle meet at a point that is equidistant from all sides. |

Median | The segment from a vertex to the midpoint of the opposite side. |

Centroid | The point of concurrency of the medians of a triangle. *Always inside a triangle* |

Altitude | The perpendicular segment from a vertex to the opposite side or an extension of the opposite side. |

Orthocenter | The point where three altitudes intersect. |

Concurrency of Medians Theorem | The medians of a triangle intersect at a point that is ⅔ of the way down from the vertex |

The Concurrency of Altitudes Theorem | The lines containing the altitudes are concurrent. |

If one side of a triangle is larger than another side of the same triangle the angle opposite the larger side is | larger than the angle opposite the smaller side. |

If one angle is larger than another angle of the same triangle the side opposite the larger angle is | larger than the side opposite the smaller angle. |

Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle are larger than the third side. |

Indirect Proof | Proving something impossible by contradiction |

Hinge Theorem | If two triangle has two sets of congruent sides and the included angle of the first is larger than the included angle of the second. The third side of the first is larger than the |

Converse of The Hinge Theorem | If two triangle has two sets of congruent sides and the third side of the first is larger than the third side of the second. The included angle of the first is larger than the included angle of the second. |