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altitude

in a triangle, a segment from a vertex of a triangle to the line containing the opposite side and perpendicular to that side

centroid

the point of concurrency of the medians of a triangle

circumcenter

the point of concurrency of the perpendicular bisectors of a triangle

concurrent lines

three or more lines that intersect at a common point

incenter

the point of concurrency of the angle bisectors of a triangle

indirect proof

in an indirect proof, one assumes that the statement to be proved is false. One then uses logical reasoning to deduce that a statement contradicts a postulate, theorem, or one of the assumptions. Once a contradiction is obtained, one concludes that the statement assumed false must in fact be true

indirect reasoning

reasoning that assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis or some other accepted fact, like a postulate, theorem, or collorary. Then, since the assumption has been proven false, the conclusion must be true

median

in a triangle, a line segment with end points that are a vertex of a triangle and the midpoint of the side opposite the vertex

orthocenter

the point of congruency of the altitudes of a triangle

perpendicular bisector

in a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side

point of concurrency

the point of intersection of concurrent lines

proof by contradiction

an indirect proof in which one assumes that the statement to be proved is false. One then uses logical reasoning to deduce a statement that contradicts a postulate, theorem, or one of the assumptions. Once a contradiction is obtained, one concludes that the statement assumed false must in fact be true