### midsegment theorm

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

### circumcenter

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

### incenter

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

### altitude

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