Triangle Relationships

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.