Triangle

Triangle

In a plane, a polygon with three sides.

For measurement purposes, we establish a base b, and a height h relative to the base.

Properties

  • A planar triangle is a convex figure.
  • The vertex opposite the side chosen as the base is sometimes called the apex of the triangle .
  • A triangle has three hauteurs, three medians, three perpendicular bisectorand three angle bisectors.
    • Altitudes:

      image52

      The three altitudes determine the orthocenter of the triangle.

    • Medians:

      image54

      The three medians intersect at the centre of gravity (the centroid) of the triangle.

    • Perpendicular bisectors:

      image56

      The three perpendicular bisectors intersect at the centre of the circle circumscribed about the triangle.

    • Angle bisectors:

      image58

      The three angle bisectors intersect at the centre of the circle inscribed in the triangle.

Formulas

  • The formula to calculate the perimeter P of a triangle with sides a, b and c is: \(P=a+b+c\).
  • The formula to calculate the area A of a triangle with a base b and an altitude h is: \(A=\dfrac{b × h}{2}\).
  • Heron’s formula can be used to calculate the area A of a triangle given the lengths of the three sides, where s is the semiperimeter of the triangle: \(A=\sqrt{s(s\space –\space a) (s\space –\space b) (s\space –\space c)}\).

Examples




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