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81 Cards in this Set
 Front
 Back
 3rd side (hint)
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 noncommon 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 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 


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


Biconditional 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
