Geometry 400 Tool Belt
Terms
undefined, object
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 Undefined Figures
 point, line and plane
 Point
 Undefined figure. Represented by a capitol, printed letter (A, B, C).
 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.
 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.
 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.
 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.
 Angles
 The union of two rays with the same endpoint (vertex)
 Figure
 a set of points
 Collinear
 on the same line
 Counter Example
 a statement that is not always true.
 Coplanar
 on the same plane
 Space
 the set of all points
 Congruent
 â€œis congruent toâ€. Same size and same shape. Tic/hash marks show that the two figures are the same size and shape
 Midpoint
 a point in the middle. A point that divides a segment into two equal parts
 Segment bisector
 a ray/line/plane/segment that contains the midpoint.
 Postulate
 a statement without proof (doesnâ€™t need proof)
 Theorem
 a theory/statement that has been proven true.
 Property
 rules of math
 Definition
 meaning
 Between
 a point is between two other points if it is on the segment connecting those two points.
 Good Diagram
 an illustration that shows nothing more and nothing less than the given information.
 Acute
 an angle whoâ€™s measure is less than 90 degrees.
 Obtuse
 an angle whoâ€™s measure is between 90 and 180 degrees.
 Right
 an angle whoâ€™s measure is exactly 90 degrees.
 Straight Angle
 angles whose measure is exactly 180 degrees.
 Complimentary Angles
 a measure of two angles whose sum adds up to 90 degrees.
 Supplementary Angles
 a measure of two angles whose sum adds up to 180 degrees.
 Adjacent Angles
 two angles with the same vertex and a common side between them.
 Vertical Angles
 two angles with the same vertex formed by opposite rays.
 Linear Pair
 two adjacent angles whose noncommon sides are opposite rays
 Inductive
 based on a conclusion that was based on observation.
 Deductive
 decision based on what you already know.
 Coordinate
 a number that goes along with a point.
 Formula
 a theorem that involves numbers
 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.
 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.
 Perpendicular Lines
 Two lines that intersect to form two right angles.
 Parallel Lines
 Coplanar lines that never intersect
 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.  Distributed Property
 a (b+c)= ab+ac
 Trichotomy Property
 If a and b are reflexive then a<b or a=b or a>b.
 Addition Property

If a=b and c=d,
a+c=b+d  Subtraction Property

If a=b and c=d,
ac=bd  Multiplication Property

If a=b and c=d,
ac=bd  Division Property

If a=b and c=d,
a/c=b/d  Conditional Statements

If, then statements.
If_____(hypothesis)
then ________(conclusion)  Converse Statements

a conditional statement formed by swapping the hypothesis and conclusion.
q>p (if q then p)  Biconditional Statements

a conditional statement combined with its converse.
p<>q  iff
 if and only if
 Negation
 the opposite (~)
 Inverse Statements

a conditional statement formed by negating both the hypothesis and the conclusion.
~p>~q  Contrapositive Statements

the negation of a converse statement.
~q>~p  Midpoint theorem
 If B is the midpoint of segment AC, then AB=1/2AC.
 Angle Bisector Theorem
 If ray BD bisects angle ABC, then anlge ABD= 1/2ABC.