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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

### 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

### perpendicular bisector

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

### 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