geometry FINALS
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a rule that is accepted without proof
postulate/axiom

the real number that corresponds to a point
coordinate

the absolute value of the difference of the coordinates of A & B
distance

two angles that share a common vertex & side but have no common interior points
adjacent angles

two adjacent angles whose noncommon sides are opposite rays.
linear pair

two angles whose sides form two pairs of opposite rays
vertical angles

a closed plane figure
polygon

in a polygon if no line that contains a side of the polygon contains a point in the interior of the polygon
convex

a polygon that is not conves
concave

the distance around a fugure
perimeter

the distance around a circle
circumference

the amount of surface covered by a figure
area

an unproven statement based on observations
conjecture

find a pattern in specific cases & then write a conjecture for the general case
inductive reasoning

a specific case for which the conjecture is false
counterexample

a logical statement that has 2 parts a hypothesis & a conclusion
conditional statement

a statement that is the opposite of the original statement
negation

uses facts definitions accepted properties & laws of logic
deductive reasoning

a = b, then a + c = b + c
addition prop



a=b & c does not = 0 then a/c = b/c
division prop

a = b ac=bc
multiplication prop

a logical arguement that shows a statement is true.
proof

has numbered statements & corresponding reasons
twocolumn proof

a statement that can be proven
theorem

all right angles are congruent
right angles congruence theorem

if two angles are supplementary to the same angle (or to congruent angles) then they are congurent
 congruent supplements theorem
 same for complements

if two angles form a linear pair then they are supplementary
LINEAR PAIR POSTULATE

vertical angles are congruent
vertical angles congruence theorem

two lines that do not intersect & are coplanar
parllel lines

two lines that do not intersect & are not coplanar
skew lines

is there if a line and a point not on the line, then there if exactly one line through the point parallel to the given line
parallel postulate

if there is a line & a point not on the line, then there is exactly one line through the point perpendicular to the given line
perpendicular postulate

a line that intersects two or more coplanar lines & different points
transversal

if two lines are parallel to the same line, then they are parallel to each other
transitive property of parallel lines

in a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope
slopes of parallel lines

two nonvertical lines are perpendicular if & only if the product of their slopes id 1
slopes of perpendicular lines

if a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other
perpendicular transversal theorem

in a plane if two lines are perpendicular to the same line, then they are parallel to each other
lines perpendicular to a transversal theorem

the original angles
interior angles

the angles that form linear pairs w/ the interior angles are the
exterior angles

the sum of the measures of the interior angles of a triangle is 180
triangle sum theorem

the measure of an exterior angle of a triangle is = tot he sum of the measures of the two nonadjacent interior angles
exterior angle theorem

a statement that can be proved easily using the theorem
corollary to a theorem

the acute angles of a right angle are complementary
corollary to the triangle sum theorem

if two angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are also congruent
third angles theorem

if two sides of a triangle are congruent then the angles opposite them are congruent
base angles theorem

if two angles of a triangle are congruent then the angles opposite them are congruent
converse of base angles theorem

if a triangle if equilateral then it is equiangular
corollary to the base angles theorem

if a triangle is equiangular, then it is equilateral
corollary to the converse of base angles theorem

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


moves every point of a figure the same direction & distance
translation

uses a line of reflection to create a mirror image of the original figure
reflection

turns a fig. around a fixed point
rotation

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

the segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side & is half as long as that side
midsegment theorem

a seg., ray, line, or plane that is perpendicular to a segment @ its midpoint
perpendicular bisector

same distance form each point
equidistant

in a plane if a point is on the perpendicular bisector of a seg. then it is equidistant from the endpoints of the seg.
perpendicular bisector theorm

in a plane if a point is equidistant from the endpoints of a seg. then it is on the perpendicular bisector of the segment
converse of the perpendicular bisector theorem

when three or more lines,rays, or segs. intersect in the same point
 concurrent
 the point is the point of concurrency

the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
concurrency of perpendicular bisectors of a triangle

the point of concurrency of the 3 perpendicular bisectors
circumcenter

if a point is on the bisector of an angle, then it is equidistant form the two sides of the angle
angle bisector theorem

if a point is in the interior of an angle & is equidistant from the sides of the angle then it lies on the bisector of the angle
converse of the angle bisector theorem

the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
concurrency of angle bisectors of a triangle

the point of concurrency of the 3 angle bisectors of a triangle
incenter

a segment from a vertex to the midpoint of the opposite side.
median of triangle

point of concurrency of the medians of a triangle
centroid

the medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
concurrency of medians of a triangle

the perpendicular segment from vertex to the opposite side or line that contains the opposite side
altitude of a triangle

the lines containing the altitudes of a triangle are concurrent
concurrency of altitudes of a triangle

the point of concurrency for ltitudes
orthocenter

the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side
triangle inequality theorem

if two sides of one triangle are congruent to two sides of another triangle & the includes angle of the 1st is larger than the included angle of the 2nd then the third side of the 1st is longer then the 3rd of the second
hinge theorem

if two sides of one triangle are congruent to two sides of another triangle & the third side of the first is longer than the third side of the second then the included angle of the first is larger than the included angle of the second
converse of the hinge theorem