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the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side
perpendicular bisector theorm
in a plane, if a point is on the perpendicular bisector of a segment, then it is equidstant from the endpoints of the segment
converse of the perpendicular bisector theorm
in a plane, if a point is equidisant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
concurrency of perpendicular bisector of a triangle
the perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle
the point of concurrency of the three perpendicular bisectors of a trianlge (equidstant from the three vertices)
angle bisector theorm
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 theorm
if a point is in the interior of an angle and is equidstant from the sides of the angle, then it lies on the angle bisector of the angle
concurrency of angle bisectors of a triangle
the angle bisector of a triangle intersect at a point that is equidistant from the sides of a triangle
the poing of concurrency of the three angle bisectors of a triangle (always lies inside the triangle)
concurrency of medians of a triangle
the medians of a triangle intersect at a point that is 2/3 of the distance from the vertex to the midpoint of the opposite side
the perpendicular segment from the vertex to the opposite side or to the line that contains the opposite side
concurrency of altitudes of a triangle
the lines containing the altitudes of a triangle are concurrent
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