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geo relations in tri

relationships and inequalities in triangles (chp. 5)

hypothesisconclusion
Any point on the perpendicular bisector of a segment... is equidistant from the endpoints of the segment.
Any point equidistant from the endpoints of a segment... lies on the perpendicular bisector of the segment.
The circumcenter of a triangle... is equidistant from the vertices of the triangle.
Any point on the angle bisector... is equidistant from the sides of the angle.
The incenter of a triangle... is equidistant from each side of the triangle.
The centroid of a triangle is located... 2/3 of the distance from a vertex to the midpoint of the opposite side.
If an angle is an exterior angle of a triangle... then its measure is greater than the measure of either remote interior angle.
If one side of a triangle is longer than another side,... then the angle opposite the longer side has a greater measure that the angle opposite the shorter side.
If one angle of a triangle has a greater measure than another angle... then the side opposite the angle with a greater measure is longer than the side opposite the lesser angle.
The sum of the lengths of any two sides of a triangle... is greater than the length of the third side.
The perpendicular segment from a point to a line... is the shortest segment from the point to the line.
The perpendicular segment from a point to a plane... is the shortest segment from the point to the plane.
(SAS inequality) If two sides of a triangle are congruent to sides of another triangle and the included angle in one triangle has a greater measure than the included side of another triangle... then the third side of the first triangle is longer than the third side of the second triangle.
(SSS inequality) If two sides of a triangle are congruent are congruent to sides of another triangle and the third side in one triangle is longer than the third side of the other,... then the angle between the pair of congruent sides in the first triangle is greater than the angle between the congruent sides in the second triangle.
Created by: m.meyer