2.  Perpendicular bisector – is a line that goes through a segment cutting it into equal parts, creating 90°angles  Perpendicular bisector theorem – if a segment is bisected by a perpendicular line then any point on the perpendicular bisector is equidistant to the end point of the segment  Converse – is a point is equidistant from the endpoint of a segment, then the point lies on the perpendicular bisector of the segment

4.  Angle bisector – line/ray that goes exactly through the half of an angle  Angle bisector theorem – if an angle is bisected by a line/ray then any point on that line is equidistant from both sides of the angle  Converse – if a given point in the interior of an angle is equidistant from the sides of the angle then it is on the bisector of the angle

6.  Concurrent – three or more lines that intersect at one point  Circumcenter – is the point of congruency in a triangle which is where the points intersect.  Concurrency of perpendicular bisectors of a triangle theorem – perpendicular bisectors of a triangle intersect in a point that is equidistant from the vertices

9.  The concurrency of angle bisectors of a triangle says that the 3 bisectors are congruent  The incenter is the point of concurrency of the angle bisectors, always inside the triangle

11.  Median – is a segments in which the endpoints are a vertex of the triangle and the midpoint of the opposite side  Centroid – is the point of concurrency of the medians of a triangle.  The centroid of a triangle is 2/3 of the distance from each vertex to the midpoint of the opposite side

13.  Altitude of a triangle – is a segment from one vertex to the opposite side so the segment is perpendicular to the side. There are 3 altitudes for any triangle, it can be inside, outside or in the triangle  Orthocenter – is the point where the three altitudes of a triangle intersect. In obtuse triangles the orthocenter is outside  Concurrency of altitudes of a triangle theorem – the three lines containing the altitudes of a triangle are congruent

16.  Midsegment of a triangle – any segment that joins the midpoint of two sides of the triangle  Midsegment theorem – a midsegment of a triangle is parallel to the side of the triangle and the length is half the length of that side

18.  Angle side relation in a triangle, the side opposite to the biggest angle will always have the longest length, the side opposite to the smallest angle will have the smallest length

20.  Exterior angle inequality – the exterior angle is greater than the non-adjacent interior angles of the triangle  Triangle inequality – any two sides of a triangle must add up to more than the 3 rd side

22.  Steps to write an indirect proof – 1. Assume that what you are trying to prove is false 2. Try to prove it using the same steps as in normal proofs 3. When you face a contradiction, you have to prove the theory true

24.  Hinge theorem – if two sides of two different triangles are congruent and the angle between them is not congruent, then the triangle with the larger angle will have the longer 3 rd side