In this activity we are going to discover some special lines in any triangle and some of their interesting properties.[br][br]Follow these instructions:[br][br][size=150][b]1. Draw any triangle[/b][/size].[br][size=150][b]2. Find the midpoint of each side using Geogebra tools.[br][/b][/size][size=150][b]3. Connect each vertex with the midpoint of the opposite side.[/b][/size]

[size=150][list][*]Each line segment joining one vertex with the midpoint of its opposite site is called a [b]median.[/b][/*][/list][list][*]The point where they intersect is called the [b]Centroid [/b]or [b]Mass Center. [/b][/*][*]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.[/*][/list][/size][br][size=150][b]4. Draw any triangle[/b][/size].[br][size=150][b]5. Find the midpoint of each side using Geogebra tools.[/b][/size][br][size=150][b]6. Draw a perpendicular line to each side passing to its midpoint.[br][/b][/size][size=150][b]7. Draw a circle with center in the intersecting point passing through one of the vertices of the triangle.[/b][/size]

[size=150][br][list][*]Each line perpendicular to one of the sides of a triangle passing through its midpoint is called [b]perpendicular bisector. [/b][/*][/list][list][*]The point where they intersect is called [b]circumcenter.[br][/b][/*][/list][/size][size=150][b][br]8. Draw any triangle[/b][/size].[br][size=150][b]9. Draw a perpendicular line to each side passing through its opposite vertex.[br][/b][/size]

[list][*][size=150]Each line perpendicular to one of the sides of a triangle passing through its opposite vertex is called [b]Altitude. [/b][/size][/*][/list][list][*][size=150]The point where they intersect is called [b]orthocenter[/b][b].[/b][/size][/*][/list][b][br][/b][size=150][b]10. Draw any triangle[/b][/size].[br][size=150][b]11. Using Geogebra tools draw the angle bisector of each vertex[br][/b][/size][size=150][b]12. Draw a perpendicular line to one of the sides of the triangle passing through the point where the angle bisectors intersect.[br]13. Draw a circle centered in the intersection point of the bisectors passing through the point where the perpendicular line and the side intersect.[/b][/size]