Median of a Triangle

Triangle means a polygon which is enclosed on three sides with three straight lines. Its angle can be obtuse or acute or right. The acute and obtuse angle combines to form an oblique triangle. Triangles can also be distinguished based on sides named scalene, isosceles, or equilateral.

The word “median” has various meanings with different operations in mathematics. It is defined as the mid-point of a data set in statistics. A median is a line segment from an interior angle of a triangle from the midpoint to the opposite side is defined in geometry.

The geometric median helps to make your life in geometry. Before knowing about the median of the triangle, let’s first know about the area. 

Area

The area is defined as the space of a polygon occupied in two dimensions. The interior space of a triangle is defined as the area of a triangle. The area is measured in square units irrespective of shape. The area is measured by length multiplied by width. The height in the area is also known as altitude. 

The formula for the area of a triangle is 

Area = ½ (base * height)

Median of Triangle

The median of a triangle is a line segment which the vertex of a triangle to the mid-point of another side. There are three medians in every triangle due to the three sides. The medians are of equal length on every side of an equilateral triangle.

When the median is drawn from the vertices of the equal angles in an isosceles triangle, then the median is of equal length. Though, the median can never be equal in a scalene triangle. The median is always in the interior of the triangle. Each median divides a triangle into two smaller ones of the equal-area while the three median divides into six smaller ones of equal area.

The centroid of a Triangle

The centroid is the point common where the three medians of the triangle cross. Centroid comprises two-thirds of each median from the median’s interior angle. Centroid sets up a 2:1 ratio for three of the medians separately. It is also the center of mass of the triangle. 

How to find the median of a triangle?

The theorem used to determine the median of a triangle is Apollonius’s Theorem. The theorem states, “In any triangle, the sum of the squares on any two sides is equal to twice the square on the median, which bisects the third side.”

The formula derived from the theorem is –

M =√2b2+ 2c2 -a2∕4

Here a, b and c denotes the length of the sides, and M is the median from interior angle A to a.

Example

Q. A pizza has been cooked in the scalene triangle whose points are named as E, A, T. You want to share to share with your friend. So, how will you divide that so that it is distributed equally?

Ans – To distribute the pizza equally, the median needs to be calculated. So, from any interior angle, just cut to the mid-point of the pizza of the opposite side. Then, this pizza can be equally distributed. 

/ Engineering, General

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