orthocenter:
the intersection of the three altitudes of the triangle.
altitude:
A line beginning at the vertex of a triangle and creating a perpendicular on the opposite leg.
Circumcenter:
where the perpendicular bisectors intersect. The circumcenter is also the center of the circle that passes through all three of the triangle's vertices
Perpendicular bisector:
for line AB it is a perpendicular line that goes through the midpoint of AB.
Circumradius:
The radius of the circle that touches the vertices of an inscribed polygon.
Thales Theorem:
states that if A, B and C are points on the circle with the line AC as the diameter of the circle, then the ∠ABC is a right angle. It is used to create Thale’s circle, which is a way to create a tangent line to any point on the circle. This is a specific case of the inscribed angle theorem.
Centroid:
where the center of mass of the triangle is. It also happens to be where the medians intersect.
Median:
line from the vertex of a triangle to the midpoint of the opposite leg.
Euler’s line
is for any non equilateral triangle. It passes through many points, including the orthocenter, the circumcenter, the centroid, and the center of the nine point circle of the triangle.
Locus:
Set of all points that share a property.
Circumcircle:
For any polygon, the circle that passes through all of the vertices of the polygon.
Rectangle:
Quadrilateral with four right angles.
The nine point circle:
(Also known as Euler’s circle and Feuerbach’s circle.) is a circle that can be constructed for any given triangle and passes through nine significant points. Those nine points are:
- The midpoint of each side of the triangle
- The foot of each altitude
- The midpoint of the segment on the altitude between the vertex and the orthocenter.