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81 Cards in this Set

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  • Back
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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 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,
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