Geometry Proof Vocabulary

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