# 8 - Remarkable lines and triangles

## Perpendicular bissector

The perpendicular bissector of a segment is the line which is perpendicular to the segment and which passes through its centre.

## Angle bisector

The angle bissector of an angle is the semi-straight line that divides the angle into two equal angles. Construction with the compass :

## Height

The height of a triangle is a line which passes through a vertex of the triangle and which intercept the opposite edge with right angle.

## Median

The 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.