Properties of the Medians| Very important Geometry theorems with Proof and examples
The point of intersection of all three Medians of the triangle is called a ‘Centroid’. The Median of a triangle is a line segment joining a vertex to the midpoint of its opposite side, thus bisecting the side.
A homogeneous triangular sheet can be balanced on its Centroid. This means that the triangle is stabilized in a horizontal position when you place its Centroid on the tip of a Pencil. Here the Centroid acts as the Centre of Gravity.
All the Medians of a triangle are concurrent (intersect at a single point), the point of concurrence is called the Centroid of the triangle. The Centroid always lies inside the triangle.
• The Centroid divides each median in the ratio of 2:1
• All the medians divide a triangle into 6 parts of equal areas.
Questions of the Day
Que 1: In an △ABC the length of all its medians AP, BQ, and CR are 6 cm, 3 cm, and 5 cm respectively then find the sum of the squares of all the sides of the triangle.
Que 2: Find the area of this triangle ABC.
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