T³ Europe Resources

Centres of a Triangle

Centres of a Triangle

Barrie Galpin

Topic:

Tags Circles, Zeros, Geometry, T3

Construct some of the centres of a triangle and investigate relationships between them, discovering the Euler Line

This activity helps students to construct the centroid, orthocentre, circumcentre and intersection of the angle bisectors. By dragging the vertices of the original triangle they can then discover that three of these centres always lie on a line.

The activity then extends to finding the Nine-point Centre and discovering that this centre also lies on the line, which is revealed to be the Euler Line.

 

During the activity students also draw the circumcircle and incircle. An extension activity investigates the ratio into which the centroid divides each median.

There is a .tns document for students to use with instructions for the constructions on a 5-page handout.