Median of a Triangle

Median is a Mathematical term that carries different meanings in different cases. In Statistics, Median is a certain value at the middle of a data set. Here, the focus is given on the definition of Median in Geometry. Triangle is a trigon with 3 vertices and 3 angles. 

The median of a triangle joins the vertex to the middle point of the triangle's opposite side. Any triangle has of three vertices and three medians. One thing is to be noted that whatever shape the triangle may have, three medians will always intersect at one point. That central is termed as the centroid of the triangle. The centroid is 2/3 of the way between each median and the median's interior angle.

Properties of Median of the Triangle 

The Median of the Triangle contains the below-mentioned properties, like

a. The three median points always head towards a single point.

b. Each of the three medians dissects the triangle in two smaller triangles with the same area.

c. The center point of the triangle is also the center of gravity of the main triangle.

d.Altogether the three medians divide the main triangle with the same area even if they hold different shapes. 

Median of a Triangle Theorem

There is a theorem called Apollonius’s Theorem that will show you the length of the median of a triangle. The formula is wordy, but it can be transformed into a simple-looking formula. 

According to Apollonius's theorem, in any triangle, the total sum of the squares of any two points is equivalent to twice the square on half of the third side together along with the twice the square on the median that divides the third side. 
The length of the Median of a Triangle can be calculated with the help of the Apollonius Theorem. 

Median of a Triangle Formula
The median of a Triangle as a formula looks like where a, b, and c are the lengths of the sides of the medians and m is the median that can be found in the interior angle.
   

The formula mentioned above is the answer to how to find the median of the triangle. 

Does the Median of a Triangle bisect the Angle?

Yes! The median of a Triangle is a bisector of the angle. Median is found to be joining the vertex of the triangle with the opposite side of the triangle. This way, the angle at the vertex is divided into two parts. 

Altitude and Median of a Triangle 

The altitude and median of a triangle is a line segment that joins the vertex of the triangle with the other side in a way that the segment remains at a perpendicular position to the opposite side. 

In the blog, we have provided you with a brief idea concerning the median of a triangle.