![]() A median is the line segment from a vertex of a triangle to the midpoint of the opposite side.The important concepts on medians and centroid are, This point of intersection of medians lies inside the triangle and is called the Centroid. The three medians pass through or intersect with each other at a single point inside the triangle G (in our figure). In the above figure, the medians from three vertices A, B and C are respectively, AD, BE and CF where D, E and F are the midpoints of the sides BC, CA and AB respectively. In other words, a median is the side bisector passing through a vertex. The following figure shows our objects of interest, the medians.Ī median is the line segment joining a vertex of a triangle and the mid-point of the opposite side. In any discussion on geometry the first thing that we need is a geometric figure. ![]() In this session we will go through the important concepts related to medians and also the mechanisms or proofs behind the concepts. Medians form one of the most important set of components in a triangle closely tied to the triangle independent of any other geometric shape.įor example another pair of important components, the incentre and the inradius inherit all the properties of a circle to enrich the concept of a triangle, whereas the medians and their intersection point, the centroid, throw more light on the the triangle independent of any other geometric shape. This point of intersection of medians is the centroid. Properties of a centroid: Three medians of a triangle always intersect at a single point inside the triangle.Segmentation ratio of medians at centroid: Each median is segmented at centroid in the ratio of 2 : 1 with lager segment towards the vertex.Second relation between median and sides of triangle: Three times the sum of squares of the length of sides equals four times the squares of medians of a triangle.First relation between median and sides of triangle: Sum of two sides is larger than the median from the common vertex.Relation between median and sides of triangle and other properties of medians
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