12 terms
Geometry Chapter 5 Vocab
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