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Geometry 400- Tool Belt


undefined, object
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Undefined Figures
point, line and plane
Undefined figure. Represented by a capitol, printed letter (A, B, C).
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.
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.
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.
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.
The union of two rays with the same endpoint (vertex)
a set of points
on the same line
Counter Example
a statement that is not always true.
on the same plane
the set of all points
“is congruent to”. Same size and same shape. Tic/hash marks show that the two figures are the same size and shape
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.
a statement without proof (doesn’t need proof)
a theory/statement that has been proven true.
rules of math
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.
an angle who’s measure is less than 90 degrees.
an angle who’s measure is between 90 and 180 degrees.
an angle who’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 non-common sides are opposite rays
based on a conclusion that was based on observation.
decision based on what you already know.
a number that goes along with a point.
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
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,
Subtraction Property
If a=b and c=d,
Multiplication Property
If a=b and c=d,
Division Property
If a=b and c=d,
Conditional Statements
If, then statements.

then ________(conclusion)
Converse Statements
a conditional statement formed by swapping the hypothesis and conclusion.
q->p (if q then p)
Bi-conditional Statements
a conditional statement combined with its converse.
if and only if
the opposite (~)
Inverse Statements
a conditional statement formed by negating both the hypothesis and the conclusion.
Contrapositive Statements
the negation of a converse statement.
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.

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