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Special lines and points in a triangle

Auteur:Gio Villalba, Sham
Onderwerp:Meetkunde
In this activity we are going to discover some special lines in any triangle and some of their interesting properties. Follow these instructions: 1. Draw any triangle. 2. Find the midpoint of each side using Geogebra tools. 3. Connect each vertex with the midpoint of the opposite side.
  • Each line segment joining one vertex with the midpoint of its opposite site is called a median.
  • The point where they intersect is called the Centroid or Mass Center.
  • If you were to construct a real triangle with uniform density (same thickness and material) that is how you find the exact point where it balances.
 4. Draw any triangle. 5. Find the midpoint of each side using Geogebra tools. 6. Draw a perpendicular line to each side passing to its midpoint. 7. Draw a circle with center in the intersecting point passing through one of the vertices of the triangle.

What can you say about the circle in point 8.?

  • Each line perpendicular to one of the sides of a triangle passing through its midpoint is called perpendicular bisector.
  • The point where they intersect is called circumcenter.
8. Draw any triangle. 9. Draw a perpendicular line to each side passing through its opposite vertex.
  • Each line perpendicular to one of the sides of a triangle passing through its opposite vertex is called Altitude.
  • The point where they intersect is called orthocenter.
10. Draw any triangle. 11. Using Geogebra tools draw the angle bisector of each vertex 12. Draw a perpendicular line to one of the sides of the triangle passing through the point where the angle bisectors intersect. 13. Draw a circle centered in the intersection point of the bisectors passing through the point where the perpendicular line and the side intersect.

What can you say about that circle?

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