# highschool geometry, algebra 2, triginometry, pre-calc/calculus

### 92 terms by Kiernan4

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### 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.

AB + BC = AC.

### complementary angles

2 angles whose sum is 90 degrees.

### supplementary angles

two angles whose sum is 180 degrees.

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

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

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

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