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92 terms

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

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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.
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