undefined term

A word without a formal definition.

point

A point has no dimension. It is represented by a dot.

line

A line has one dimension. It is represented by a line with two arrowheads.

plane

A plane has two dimensions. It is represented by a shape that looks like a floor or a wall.

collinear points

Points that lie on the same line.

coplanar points

Points that lie in the same plane.

defined terms

Terms that can be described using known words.

line segment/endpoints

Part of a line that consists of two points, called endpoints, and all the points on the line between the endpoints.

ray

The ray "AB" consists of the endpoint "A" and all points on line "AB" that lie on the same side of "A" as "B."

opposite rays

2 rays that have the same endpoint and go in opposite directions forming a line.

postulate, axiom

A rule that is excepted withought proof.

theorem

A rule that can be proved.

coordinate

The real number that corresponds to a point.

distance

The distance between two points "A" and "B," written as "AB," is the absolute value of the difference of the coordinates of "A" and"B."

between

When three points are collinear, you can say that one point is between the other two.

congruent segments

Line segments that have the same length.

segment addition postulate

AB + BC = AC.

complementary angles

2 angles whose sum is 90 degrees.

supplementary angles

two angles whose sum is 180 degrees.

adjacent angles

two angles that share a common vertex or side, but have no common interior points.

linear pair

two adjacent angles are a linear pair if their noncommon sides are opposite rays.

vertical angles

two angles are vertical angles if their sides form two pairs of opposite rays.

conjecture

an unproven statement that is based on observations.

inductive reason

the process of finding a pattern for specific cases and then writing a conjecture for the general case.

counterexample

a specific case for which the conjecture is false.

conditional statement

a logical statement that has 2 parts: a hypothesis and a conclusion.

if-then-form

a form of a conditional statement in which the "if" part contains the hypothesis and the "then" part contains the conclusion.

hypothesis

the "if" part of a conditional statement.

conclusion

the "then" part of a conditional statement.

negation

the opposite of the original statement.

converse

the part of a conditional statement that is formed by negating both the hypothesis and conclusion.

inverse

the part thats formed by negating both the hypothesis and the conclusion.

contra-positive

the part that is formed by writing the converse and then negating both the hypothesis and the conclusion.

equivelent statements

2 statements that are both true or both false.

perpendicular lines

2 lines that intersect to form a right angle.

biconditional statement

a statement that contains the phrase "if, and only if"

deductive reasoning

using facts, definitions, excepted properties, and laws of logic to form a logical argument.

line perpendicular to a plane

if, and only if, the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

postulate 1:

through any two points there exists exactly one line

postulate 2:

a line contains at least 2 points

postulate 3:

if 2 lines intersect, then their intersection is exactly one point

postulate 4:

~postulate #4 was executed before its people and sadly, no longer exists :(

postulate 5:

through any 3 noncollinear points there exists exactly one plane

postulate 6:

a plane contains at least 3 noncollinear points

postulate 7:

if 2 points lie in a plane then the line containing them [also] lies in the plane

postulate 8:

if two planes intersect, then their intersection is a line

postulate 11 1/2: (don't ask me how)

through any 3 noncollinear points, there exists exactly one plane

addition property

if a = b, then a+c = b+c.

subtraction property

if a = b, then a - c = b - c.

multiplication property

if a = b, then a x c = b x c.

division property

if a = b, then a\c = b\c.

substitution property

if a = b, then "a" can be subbed for "b"

proof

A logical argument that shows a statement is true.

two-column proof

Has numbered statements and corresponding reasons that show an argument in logical order.

Theorem

a statement that can be proven

parallel lines

two lines that do not intersect and are co-planar

skew lines

two lines that do not intersect and are NOT coplanar

parallel planes

two planes that do not intersect

transversal

a line that intersects two or more coplanar lines at different points

corresponding angles

two angles that have corresponding positions

alternate interior angles

two angles that lie between the two lines and on opposite sides of the transversal

alternate exterior angles

two angles that lie outside the two lines and on opposite sides of the transversal

consecutive interior angle

two angles that lie between the two lines and on the same side of the transversal

postulate 15:

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

slope-intercept form

the general form of a linear equation in slope-intercept form is 'y=mx+b' where "m" is the slope and "b" is the Y-intercept

standard form

the general form of a linear equation in standard form is Ax+By=c, where "A" and "B" are not both zero

distance from a point to a line

the length of the perpendicular segment from the point to the line

triangle

a polygon with 3 sides

interior angles

when the sides of a polygon are extended, the original angles are the interior angles

exterior angles

when the sides of a polygon are extended, the angles that form linear pairs with the interior angles are the exterior angles

corollary to a theorem

a statement that can be proved easily using a theorem

congruent figures

where all the parts of one figure are congruent to the corresponding parts of the other figure

corresponding parts

in congruent polygons, the corresponding parts are the corresponding sides and the corresponding angles

leg of a right triangle

in a right triangle, a side adjacent the right angle is called a leg

hypotenuse

in a right triangle, the side opposite the right angle is called the hypotenuse

flow proof...

DONT CARE......

legs

the two congruent sides of an isosceles triangle

vertex angle

the angle formed by the legs in an isosceles triangle

base

the side of an isosceles triangle that is not a leg

base angles

the two isosceles angles congruent to the base

transformation

an operation that moves or changes a geometric figure in some way to produce a new figure

image

the new figure produced by a transformation

translation

moves every point of a figure the same distance in the same direction

reflection

uses a "LINE OF REFLECTION" to create a mirror image of the original figure

rotation

turns a figure about a fixed print, called the "CENTER OF ROTATION"

midsegment of a triangle

a segment that connects the midpoints of two sides of a triangle

coordinate proof

involves placing geometric figures in a coordinate plane

perpendicular bisector

a segment, ray, line, or plane that is perpendicular to a segment at its midpoint

equidistant

if a point is the same distance between each two figures

concurrent

when three or more lines/rays or segments intersect in the same point

point of concurrency

the point of intersection of concurrent lines, rays, or segments.

circumcenter

the point of concurrency of the three bisectors of a triangle