Perpendicular bissectorThe perpendicular bissector of a segment is the line which is perpendicular to the segment and which passes through its centre.
Angle bisectorThe angle bissector of an angle is the semi-straight line that divides the angle into two equal angles. Construction with the compass :
HeightThe height of a triangle is a line which passes through a vertex of the triangle and which intercept the opposite edge with right angle.
MedianThe median of triangle passes through a vertex and intercepts the opposite edge at its centre.
A lovely diagram which summarizes everything (to be memorized) :
In a triangle :
- The intersection of 3 altitudes is called the orthocenter.
- The intersection of 3 medians is called the centroid.
- The intersection of 3 angle bissectors is the centre of the inscribed circle.
- The intersection of 3 perpendicular bissectors is the centre of the circumscribed circle.
The centre of gravity of a triangle is always located at the 2 thirds of each median starting from the vertices of the triangle.
See also : geometry on fmaths.com