In this video, let's discuss medians of a triangle.
Say you have triangle ABC over here.
Now let's identify point B on AC, such that AP is equal to P.c or B is the midpoint of line segment
AC.
All right.
Now let's join point B to B now.
BP is what we call a median.
So you can see that a median is a line that goes through a vertex and it joins the midpoint of the opposite
side.
So it's joining a vertex to the midpoint of the opposite side.
So over here, be the vertex and B is the midpoint of the opposite side.
That is AC.
So when you join BNP, you get a median already.
Now, how many medians does a triangle have?
You know that a triangle has three vertices.
Therefore it will have three medians.
Let's draw the other mutants.
So this median that is C R, right.
It goes through Vertex C and it.
Joins the midpoint of the opposite side, A, B to C, right, that's here, what about AQ use the midpoint
of B, C and Q is joined to Vertex eight, that's AQ.
So these are the three millions of Triangle ABC.
And you will see that the Marines also intersect at that point.
Right.
And this point is called the centroid.
So we have learned that the meeting point of the altitude's of a triangle is called Auto Center.
And over here we have learned that the meeting point of the median of a triangle is called the centroid.
The median divides a triangle into two triangles of equal area.
Now let's try to understand why that is.
For example, AQ is a median, right?
So we we're seeing that area of Triangle A, B, Q is equal to area of Triangle E, you see.
Let's see why that is.
Over here, we know that BQ is equal to QC because cuz the midpoint of B.C..
Right.
And let's drop it perpendicular from point A to site B.C..
That would look like this, and this is the height of this triangle from point A, right?
So what is the area of Abiquiu that would be half into to into it?
And what is the area of see, that's half in do you see into it?
And we know is look you see.
So we see that this area is equal to this area.
Right.
So that's why a median divides a triangle into two triangles of equal area.
All right.
Now, what about the centroid?
There is an interesting property about the centroid also that we make some space over here.
The centroid divides each median in the ratio, two is two one, for example, over here we have the
centroid as all now as per this property.
What we can say is that a wall divided by OCU is divided by two by one.
Right.
Because this median the centroid is dividing this median equal in the ratio.
Two is two one.
Let's quickly revise one of the things that we've learned about medians and median is a line segment
that joins a vertex to the midpoint of the opposite side.
Right.
All right.
We have seen that a triangle has three mutant's.
We have seen that a median divides the triangle into two triangles of equal area.
And we have seen that the meeting point of the median is called centroid and the centroid divides each
median in the ratio.
Two is two one.
All right.
So even Bill by OPIS is equal to by one.
And you can say see or by or is equal to two by one.