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points that lie on the same line

collinear

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points that do not lie on the same line

noncollinear

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a mathematical statement that can be proved

theorem

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an unproved assumption

postulate

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

opposite rays

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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

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

altitude

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

auxiliary line

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

convex polygon

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lying in the same plane

coplanar

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the length of the shortest path between two objects

distance

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the first and fourth terms of a proportion

extremes

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the point of intersection of a line and a plane

foot

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the second and third terms of a proportion

means

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the point of concurrency of the altitudes of a triangle

orthocenter

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

circumcenter

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the point of concurrency of the medians of a triangle

centroid

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an equation stating that two or more ratios are equal

proportion

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a quotient of two numbers

ratio

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a polygon that is both equilateral and equiangular

regular polygon

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two lines that are not coplanar

skew lines

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