# Triangle Relationships

### By: Kammie,Megan,Kennedy,Logan

## Vocab

__Triangle Midsegments of Triangles__- If a segment joins the midpoint of two sides of a triangle, then they are parallel to the third side and its half as long.__Perpendicular and Angle Bisector__- If a point lies on the perpendicular bisector bisector of a segment then its equal distance from the endpoint of the segment.__Angle Bisector Theorem__- If a point is on an angle bisector, then it is equal distance from the side of the angle.__Concurrency of Perpendicular Bisectors__- perpendicular bisectors of the sides of a triangle are concurrent and are equal distance from the vertices.__Circumcenter:__center of a circle__Concurrency of Angle Bisectors__- Incenter__Medians__- are concurrent at a point that is 2/3 the distance from each vertex.__Centroid__- is the point of concurrency (Center of Gravity)__Altitudes__- are perpendicular segments from the vertex of the triangle to the line containing the opposite side__Orthocenter__- is the point of concurrency. It can be inside or outside the triangle.__Triangle Inequalities with One Triangle-__if two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.__Is The Converse True?__- If the larger angle lies opposite the longer side, then the sides are not congruent.__Triangle Inequality Theorem__: The sum of the----------of any two sides of a triangle is greater than the length of the third side.