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### 81 Cards in this Set

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 Undefined Figures point, line and plane 3 Point Undefined figure. Represented by a capitol, printed letter (A, B, C). definition Line Undefined figure. Common definition: a set of infinite points in a straight pattern. Represented by naming any two points on it with a line over it OR a lowercase cursive letter. definition Plane A flat figure with infinite length and width but has no figure. Drawn as a parallelogram. Represented by naming at least 3 points in clock or counter clockwise patter. Named with a capitol cursive letter. definition Ray A piece of a line with one endpoint. Represented by naming endpoint first and then any other point on it. A ray must be drawn on the top of the named letters and it must be pointing to the right. definition Segment A piece of a line with two end points. Represented by naming both points in the segment. Must have a line segment on top of the represented letters. definition Angles The union of two rays with the same endpoint (vertex) definition Figure a set of points definition Collinear on the same line definition Counter Example a statement that is not always true. definition Coplanar on the same plane definition Space the set of all points definition Congruent “is congruent to”. Same size and same shape. Tic/hash marks show that the two figures are the same size and shape definition Midpoint a point in the middle. A point that divides a segment into two equal parts definition Segment bisector a ray/line/plane/segment that contains the midpoint. definition Postulate a statement without proof (doesn’t need proof) definition Theorem a theory/statement that has been proven true. definition Property rules of math definition Definition meaning definition Between a point is between two other points if it is on the segment connecting those two points. definition Good Diagram an illustration that shows nothing more and nothing less than the given information. definition Acute an angle who’s measure is less than 90 degrees. definition Obtuse an angle who’s measure is between 90 and 180 degrees. definition Right an angle who’s measure is exactly 90 degrees. definition Straight Angle angles whose measure is exactly 180 degrees. definition Complimentary Angles a measure of two angles whose sum adds up to 90 degrees. definition Supplementary Angles a measure of two angles whose sum adds up to 180 degrees. definition Adjacent Angles two angles with the same vertex and a common side between them. definition Vertical Angles two angles with the same vertex formed by opposite rays. definition Linear Pair two adjacent angles whose non-common sides are opposite rays definition Inductive based on a conclusion that was based on observation. definition Deductive decision based on what you already know. definition Coordinate a number that goes along with a point. definition Formula a theorem that involves numbers definition Points Postulate Space contains at least 4 noncoplanar, noncollinear points. A plane contains at least 3 noncollinear points. A line contains at least 2 points. Line Postulate Two points are contained in one and only one line. Plane Postulate Three noncollinear points are contained in one and only one plane. Flat Plane Postulate If two points are contained in a plane, the line through them is contained in the same plane. Plane Intersection Postulate If two planes intersect, they intersect a line. Ruler Postulate For every pair of points, there is a unique positive real number called the distance between them. Segment Construction Postulate On any ray, there is exactly one point at a given distance from the endpoint of a ray. Segment Addition Postulate If P is between A and B, then AP+BP=AB. Midpoint Postulate A segment has exactly one midpoint. Protractor Postulate The measure of an anhle is a positive real number. Angle Construction Postulate Let H1 be a half plane with edge ray PA. There is exactly one ray, ray PB with B, in H1 such that angle APB has a given measure. Segment Construction Postulate with angles. Angle Addition Postulate If B is in the interior of angle APC then the mAPB+mBPC=mAPC. Angle Bisector Postulate An angle has exactly one bisector. Supplement Postulate The angles in a linear pair are supplementary. theorem Two intersecting lines are always coplanar. theorem A line and a point on the line are always on the same plane. theorem No matter what, the measure of an angle is always 180 degrees. theorem D = l C1 – C2l theorem Midpoint = C1 + C2/2 theorem Vertical angles are congruent theorem All right angles are congruent Perpendicular Lines Two lines that intersect to form two right angles. definition Parallel Lines Coplanar lines that never intersect definition theorem Two intersecting lines intersect at one and only one point Reflexive Property a=a AB=AB RS+CD=RS+CD Symmetric Property If a=b, then b=a. If RS=CD, then CD=RS. Transitive Property If a=b and b=c, then a=c. If AB=CD and CD=8, then AB=8. Substitution Property If a=b and a=c then b=c. - If two things are equal, whenever you see one, you may substitute. - If two things are equal to the same thing, then they're equal to eachother. IMPORTANT TO KNOW Distributed Property a (b+c)= ab+ac Trichotomy Property If a and b are reflexive then ab. Addition Property If a=b and c=d, a+c=b+d Subtraction Property If a=b and c=d, a-c=b-d Multiplication Property If a=b and c=d, ac=bd Division Property If a=b and c=d, a/c=b/d theorem Congruence of segments and angles are reflexive, symmetric, and transitive. theorem Supplements of congruent angles are congruent. Compliments of congruent angles are congruent. theorem Supplemens of the same angle are congruent. Compliments of the same angle are congruent. Conditional Statements If, then statements. If_____(hypothesis) then ________(conclusion) definition Converse Statements a conditional statement formed by swapping the hypothesis and conclusion. q->p (if q then p) definition Bi-conditional Statements a conditional statement combined with its converse. p<->q definition iff if and only if definition Negation the opposite (~) definition Inverse Statements a conditional statement formed by negating both the hypothesis and the conclusion. ~p->~q definition Contrapositive Statements the negation of a converse statement. ~q->~p definition C~C Midpoint theorem If B is the midpoint of segment AC, then AB=1/2AC. do not say midpoint theorem in proofs, simply say "midpoint" theorem If the angles of a linear pair are congruent, then the lines containing their sides are perpendicular. Angle Bisector Theorem If ray BD bisects angle ABC, then anlge ABD= 1/2ABC. state as "angle bisector" in proofs