Important Points of Triangles

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As can be seen in the illustration below, it is possible to trace four segments in a triangle, each with different characteristics. From these four different types of triangle divisions, we can find four important points in the triangle. The table presents a summary of the main characteristics of these points.

  • Altitude: draw a line at right angles to a side and going through the opposite corner.
  • Angle bisector: draw a line from a corner so that it splits the angle in half.
  • Median: draw a line from a corner to the midpoint of the opposite side.
  • Perpendicular bisector: draw a line at right angles to the midpoint of each side.
Important lines of a Triangle

OrthocenterOrthocenterIntersection point of the 3 altitude.The orthocenter is in the inner region of the triangle if this is a acute triangle, coincides with the vertex of the right angle if it is a right triangle and lies outside the triangle in the case of this being a obtuse triangle.
IncenterIncenterIntersection point of the 3 angle bisectorThe incenter is the center of a circle inscribed in the triangle. Therefore, it is at the same distance from all its sides.
CentroidCentroidIntersection point of the 3 medianThe centroid is the center of gravity of the triangle. If we suspend a triangle through its centroid, it stays in balance. This point is at a distance of two-thirds from the median to the corresponding vertex.
CircumcenterCircumcenterIntersection point of the 3 perpendicular bisectorThe circumcenter is the center of a circumference circumscribed in the triangle. Therefore, it is at the same distance from the three vertices.

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