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The Triangles and its Properties

    Medians of a Triangle

    Two Special Triangles : Equilateral and Isosceles

    What Have We Discussed ?

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7th class > The Triangles and its Properties > Medians of a Triangle

Medians of a Triangle

Given a line segment, we know how to find its perpendicular bisector by paper folding. Let us simulate paper folding above. Select a vertex B and drag towards C. That will give you the perpendicular bisector of BC.

The folded crease of the paper meets BC at D,its mid-point.Join the line segment AD.

The line segment AD, joining the mid-point of BC to its opposite vertex A, is called a median of the triangle. Consider the sides AB and CA and find two more medians of the triangle. A median connects a vertex of a triangle to the mid-point of the opposite side. Thus, a triangle will have a total of medians.

Triangle ABC with AD median (which bisects side BC)
Triangle ABC with AD median (which bisects side BC)

Think : Does a median lie wholly in the interior of the triangle? .

Here you can see a triangle as well as the midpoints of its three sides.

A median of a triangle is a line segment that joins a vertex and the midpoint of the opposite side. Draw the three medians of this triangle. What happens as you move the vertices of the triangle?

It seems like the medians always . This point is called the centroid.

Medians always divide each other in the ratio 2:1. For each of the three medians, the distance from the vertex to the centroid is always as long as the distance from the centroid to the midpoint.