Education Technology

The Euler Line and its Ratios

Activity Overview

In this activity, students will explore the Euler Line of a triangle. Students will discover that the centroid, circumcenter, and orthocenter are collinear. Students will also discover that if the triangle is isosceles, then the centroid, circumcenter, incenter, and orthocenter are all collinear. Students will also look at ratios involved in the Euler line.

Key Steps

  • Image

    On page 1.3, students are given acute 􀁕ABC. They are asked to construct the centroid, circumcenter, incenter, and the orthocenter and label them Ce, Ci, I, and O, respectively.