math
7th Grade - Geometry

7th Grade lesson

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.mediator

Angle bisector

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

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.hauteur issue d

Median

the median of a triangle 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) :
height bisecting line median and mediator


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.

inscribed circle
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



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Remarkable lines

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