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points that lie on the same line

collinear

points that do not lie on the same line

noncollinear

a mathematical statement that can be proved

theorem

an unproved assumption

postulate

two collinear rays that have a common endpoint and extend in different directions

opposite rays

a pair of angles such that the rays forming the sides of one and the rays forming the sides of the other are opposite rays

vertical angles

a perpendicular segment from a vertex of a triangle to the opposite side

altitude

a line introduced into a diagram for the purpose of clarifying a proof

auxiliary line

a polygon in which each interior angle has a measure less than 180

convex polygon

lying in the same plane

coplanar

the length of the shortest path between two objects

distance

the first and fourth terms of a proportion

extremes

the point of intersection of a line and a plane

foot

the second and third terms of a proportion

means

the point of concurrency of the altitudes of a triangle

orthocenter

the point of concurrency of the perpendicular bisectors of the triangle's sides

circumcenter

the point of concurrency of the medians of a triangle

centroid

an equation stating that two or more ratios are equal

proportion

a quotient of two numbers

ratio

a polygon that is both equilateral and equiangular

regular polygon

two lines that are not coplanar

skew lines