It's All About Geometry

Corazon Bautista, Aug 2, 2015

This book will be a collection of several interesting topics in Geometry form points, lines, planes, to surfaces that can hopefully help students, teachers, and others, visualize and conceptualize geometric ideas and structures. It is my desire that everyone sees and enjoys the beauty and wonders of math through the logic of deductive reasoning. I welcome comments and suggestions. Thanks for viewing.


  • 1. Construction of the Euler Line
  • 2. Nine-Point Circle tangent to inscribed circle and excircles
  • 3. Inscribed and Circumscribed Circles in a Triangle
  • 4. Inscribed and Circumscribed Regular Polygons
  • 5. Nine-Point Circle
  • 6. Incircles/excircles
  • 7. Exploring Proportions in Triangles
  • 8. Midsegments in a Triangle
  • 9. Investigating Midsegments in a Triangle
  • 10. Investigating Incenter & Circumcenter in a Triangle

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Construction of the Euler Line

[b]Euler line[/b] of a triangle is the straight line that contains the [i]circumcenter[/i], the [i]centroid[/i], and the [i]orthocenter[/i] of the triangle. [br][br]Recall... [i]circumcenter[/i] is the point of concurrency of the perpendicular bisectors of a triangle;[br] [i]centroid[/i] is the point of concurrency of the medians of a triangle;[br] [i]orthocenter[/i] is the point of concurrency of the altitudes in a triangle.[br][br]The applet below shows the [b]Euler line[/b] of triangle [i]ABC[/i] that contains its [i]centroid, G[/i], [i]circumcenter, J[/i], and [i]orthocenter, I[/i]. [br]Drag any of the vertices of triangle [i]ABC[/i] and observe the movement of these points, [i]G, J[/i], and [i]I[/i], in relation to the corresponding change in the triangle. [br]In addition, compare the distances from the centroid to the orthocenter and from the centroid to the circumcenter.
Construction of the Euler Line
– Corazon Bautista

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