Bisector Theorems
In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Perpendicular Bisector Theorem
The centroid of a triangle is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Centroid Theorem
A segment from the vertex to the midpoint of the opposite side. The 3 medians of a triangle are concurrent. The point of concurrency, called the centroid, is inside the triangle.
Median of a triangle
In a plane, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector.
Converse of the perpendicular bisector theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side.
Triangle Inequality Theorem
The centroid of a triangle is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Centroid Theorem
If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.
Angle Bisector Theorem
If one angle of a triangle is larger than another angle, then the side opposite of the larger angle is longer than the side of the smaller angle.
Triangle Larger Angle Theorem
The incenter of a triangle is equidistant from the sides of the triangle.
Incenter Theorem
If a point is in the interior of an angle and is equidistant from the two sides of the angle, then it lies on the angle bisector.
Converse of The Angle Bisector Theorem
If 2 sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the 1st is larger than the included angle of the 2nd, then the 3rd side of the first is larger than the 3rd side of the 2nd and the included angle is larger.
The lines containing the altitudes of a triangle are concurrent.
Orthocenter
Segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is 1/2 as long as that side.
Triangle Midsegment Theorem
The circumcenter of a triangle is equidistant from the vertices of the triangle.
Circumcenter Theorem
The point inside the triangle that is equidistant from each vertex.
Circumcenter