adjacent angles
share a vertex, have common side, no common interior points
vertical angles
Two nonadjacent angles formed by two intersecting lines
complementary angles
two angles whose sum is 90
supplementary angles
two angles whose sum is 180
linear pair
supplementary angles that are adjacent
perpendicular lines
two lines that meet at right angles
perpendicular bisector
forms a right angle with a line segment
distance from a point to a line
segment containing the point is perpendicular to the line
point
location in space represented as a dot with a capital letter
line
infinite set of points extending in two directions
plane
flat surface that extends infinitely
line segment
portion of a line that has a beginning and an end; it can be measured
ray
has a beginning but not an end
union
joining of objects
angle
union of two rays that intersect at the vertex
midpoint
point on a segment that divides into two segments equal in length
degree
unit that measures an angle
acute angle
angle that measures less than 90
right angle
angle that measures exactly 90
obtuse angle
angle that measures more than 90 but less than 180
straight angle
angle that measures exactly 180
opposite rays
two rays that have a common vertex and form a straight line
reflex angle
measures more than 180 and less than 360
interior
set of points that lay inside the rays that forms an angle
exterior
set of points that lay outside the rays that form an angle
angle bisector
segment, ray, or line that divides an angle into two congruent angles
polygon
closed figure
triangle
three sided polygon
scalene triangle
triangle with three sides of unequal length
isosceles triangle
a triangle with at least two sides of equal length
equilateral triangle
triangle with three sides of equal length
acute triangle
triangle containing three acute angles
equiangular triangle
triangle containing three sides equal in measure
obtuse triangle
triangle containing one obtuse angle
right angle
triangle containing one right angle
altitude
segment that joins a vertex to the side opposite the vertex and is perpendicular to that side
median
segment that a vertex to the midpoint of the opposite side
axiom
statement accepted as true without proof
reflexive postulate
a quantity is equal to itself
transitive postulate
if two quantities are equal to the same quantity, then they are equal to each other
symmetric postulate
an equality may be reversed
addition postulate
if equal quantities are added to equal quantities, then their sums are equal
subtraction postulate
if equal quantities are subtracted from equals, then their differences are equal
multiplication postulate
if equal are multiplied by equals, then their products are equal
division postulate
if equals are divided by equals, then their quotients are equal; halves of equal quantities are equal
inductive reasoning
reasoning from the specific to the general
deductive reasoning
reasoning from the general to the specific
theorem
a statement that is proven true by deductive reasoning
segment addition
the whole segment is equal to the sum of its smaller segments
angle addiction
the whole angle is equal to the sum of its smaller angles
intersection of lines theorem
if two lines intersect, then the vertical angles formed are congruent
supplements theorem
supplements of the same angle are congruent
right angle theorem
all right angles are congruent
supplementary theorem
if two angles are congruent and supplementary, then they are right angles
Congruent adjacent angles theorem
if two intersecting lines form congruent adjacent angles, then the lines are perpendicular
perpendicular lines theorem
perpendicular lines form congruent angles
complements theorem
complements of congruent angles or of the same are congruent
complements of the same angle theorem
complements of the same angle are congruent