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# Triangle Segments

### Special segments of a triangle, points of intersection, inequalities of triangle

Vocab wordDefinition
Angle bisector splits an angle into congruent parts
Perpendicular bisector splits a segment at its midpoint perpendicularly
Median a segment that connects a vertex of a triangle to the midpoint of the opposite side
Altitude a segment of a triangle that goes from a vertex perpendicularly to the opposite side
Midsegment a segment in a triangle that connects two midpoints
Midpoint a point in the middle of a segment that cuts it into two congruent parts
Orthocenter the point of intersection of the altitudes
Circumcenter the point of intersection of the perpendicular bisector
Incenter the point of intersection of the angle bisectors
Centroid the point of intersection of the medians
Center of inscribed circle Incenter
Center of circumscribed circle Circumcenter
2/3 the distance from vertex to midpoint Centroid
Equidistant from the sides of a triangle Incenter
Equidistant from the vertices of the triangle Circumcenter
Triangle Inequality Theorem Two sides of a triangle must add up to be bigger than the third side
Largest side of a triangle Opposite the largest angle
Smallest side of a triangle Opposite the smalled angle
Largest angle of a triangle Opposite the largest side
Smallest angle of a triangle Opposite the smallest side
Hinge Theorem If 2 sides of 2 triangles are congruent and the included angle of the first is bigger, then the third side of the first is bigger
Hinge Theorem Converse If 2 sides of 2 triangles are congruent and the third side of the first is bigger, then the included angle of the first is bigger
Direct Proof Using properties, definitions, postulates and theorems to prove something directly
Indirect Proof Temporarily assuming the opposite of what you are trying to prove to reach a contradiction
Created by: jenkroesen