Triangles and its properties


Medians & Altitudes:


Median of a triangle

A line segment, joining a vertex to the mid-point of the side, opposite to that vertex, is called the median of a triangle. In the figure given below, AD is the median, dividing BC into two halves, such that, DB = DC.


Properties

1)A triangle can have only three medians, all of which intersect at a point called ‘centroid’.

2)The centroid divides the triangle into six smaller triangles of equal area.

3)A median divides the area of the triangle in half.


Altitude of a triangle

Altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.


properties of Altitude

1)A triangle can have only three Altitudes, all of which intersect at a point called ‘ortho-centre’.

2)The altitudes can be inside or outside the triangle, depending on the type of triangle.

3)The altitude makes an angle of 90° to the side opposite to it.