## Glossary of Geometry 400- Tool Belt

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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
- “is congruent to”. 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 (doesn’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 who’s measure is less than 90 degrees.

- Obtuse
- an angle who’s measure is between 90 and 180 degrees.

- Right
- 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

- 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,

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

- 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)

- Bi-conditional 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.