Altitude And Median Of A Triangle

You are already aware of the term ‘triangle’ and its properties. Before exploring more about them, let us go through some of their basic properties. A triangle is a three-sided polygon which has 3 vertices and 3 sides enclosing 3 angles. Based on the length of its sides, a triangle can be classified into scalene, isosceles and equilateral based on the measure of its angles, it can be acute-angled, obtuse-angled or right-angled triangle. The sum of interior angles in a triangle is 180 degrees. Having learnt that, in this article, we introduce you to two more terms- altitude and median of triangle.

Median of Triangle

Median Of Triangle

A median of triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex. In the figure, AD is the median that divides BC into two equal halves, that is, DB = DC.

Properties of median of a triangle:

Median Of A Triangle

  • Every triangle has 3 medians, one from each vertex. AE, BF and CD are the 3 medians of the triangle ABC.
  • The 3 medians always meet at a single point, no matter what the shape of the triangle is.
  • The point where the 3 medians meet is called the centroid of the triangle. Point O is the centroid of the triangle ABC.
  • Each median of a triangle divides the triangle into two smaller triangles which have equal area.
  • In fact, the 3 medians divide the triangle into 6 smaller triangles of equal area.

Altitude of Triangle

An altitude of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles.

Altitude of Triangle

Properties of altitudes of a triangle:

  • Every triangle has 3 altitudes, one from each vertex. AE, BF and CD are the 3 altitudes of the triangle ABC.
  • The altitude is the shortest distance from the vertex to its opposite side.
  • The 3 altitudes always meet at a single point, no matter what the shape of the triangle is.
  • The point where the 3 altitudes meet is called the ortho-center of the triangle. Point O is the ortho-center of the triangle ABC.
  • The altitude of a triangle may lie inside or outside the triangle.

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Practise This Question

If ΔABCΔDEF, AB = 5 cm, BC = 6 cm, AC = 7 cm, then the length of EF is: