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# ch.5 Theorems

### Theorems Ch. 5

midsegment theorem the segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle.
Perpendicular bisector theorem if a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular bisector theorem if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Concurrency of Perpendicular bisector theorem the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
Angle bisector theorem if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
Converse of the angle bisector theorem if a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.
Concurrency angle bisector theorem the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
concurrency of medians of a triangle the medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
concurrency of altitudes of a triangle the lines containing the altitudes of a triangle are concurrent.
___________ If one side of a triangle is larger than another side, them the angle oppositethe longer side in larger than the angle opposite the shorter side.
___________ Of one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
triangle inequality theorem the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Hinge theorem it two sides of one triangle are congruent two sides of another triangle, and the included angle of the first is larger than the included angle of the second, them the third side of the first is longer than the the third side of the first of the first is
Converse of the hinge theorem if 2 sides of one triangle are congruent to 2 sides if another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
Created by: the cat