1. Median of a triangle

Triangle
    A triangle is a closed figure made by three line segments. It has three vertices, three sides and three angles.

A triangle ABC is given having three vertices A, B, C and three sides AB, BC, CA and three angles are  ∠ABC,  ∠ BCA,   ∠CAB.

Classification of triangles:
1.    With respect to angles are:
    (a)     Acute-angled triangles 
    (b)     Obtuse-angled triangles 
    (c)     Right-angled traingles 

(a)     Acute-angled triangles

A triangle in which measurement of each of the three angles are less than 90°.

(b)     Obtuse-angled triangle :

A triangle in which one angle is obtuse angle i.e. greater than 90° but less then 180°.

(c)     Right-angled triangle:

A triangle in which one angle is exactly 90°.
        •    The side opposite to the right angle is called the hypotenuse.
        •    The other two sides are called as the legs of the right-angled triangle (or base and perpendicular).
        •    In the given figure AC is the hypotenuse and AB and BC are the legs of  DABC.

Chapter 6  

Triangle and its properties

Median of a triangle

Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

A median connects a vertex of a triangle to the mid-point of the opposite side.
In the ∆ ABC, the line segment AD joining the mid-point of BC to its opposite vertex A is called a median of the triangle.

Properties of Median of a Triangle

Every triangle has exactly three medians one from each vertex and they all intersect each other at the triangle's centroid.

• 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. 

In ∆ ABC, three medians are AD, CE and BF and they are intersecting the point O which is centroid of the triangle.