Euler's Discovery

Sam Ancona
Given these tools, construct a triangle with an orthocenter, circumcenter, and centroid to form Euler's discovery. Remember: Orthocenter- When the perpendicular bisector of side "a" connects to vertex "A" on the other side of the triangle repeated for each side and vertex of the triangle. Circumcenter- When the perpendicular bisectors of each side of the triangle (being equidistant from the adjacent vertices) intersect. Centroid- The exact center of a triangle where three lines going through the midpoints on each side intersect. How to draw your triangle: 1. Click on the polygon tool (the third tool from the left) and draw any triangle of your choosing 2. Double-click on the wrench tool arrow (very last tool on the right) and choose "centroid." Then, click on each of the triangle's vertices. A point should appear in the middle of the triangle. 3. Repeat part 2 for the orthocenter and circumcenter on the same triangle as part 1
What do you notice about the three points in the triangle? What happens when the vertices of the triangle are moved from where you originally placed them? What do you think is the cause of this? What is Euler's discovery?