In this video, let's discuss the midpoint theorem, this is quite a useful theorem in many questions.
Now, over here you have a triangle, ABC.
Now let's join the midpoints of ABC and AC.
Let me be the midpoint of ABC and to be the midpoint of AC.
All right, so we have joined the midpoint of Ebbe and Acey, right, because PE's the midpoint of a
particular Beeby and because Q is the midpoint of Acee, AQ is a galaxy now as per the midpoint theorem.
If this is the case, then P Q will be parallel to B C that's one result.
And the second result is P, Q will be half of B, C that is the length of P, Q If that is A then the
length of B, C will be to A.
All right, so over here, we have got two interesting results using the midpoint theorem, let's learn
a few more interesting properties on triangles.
The next theorem that we discuss is the proportionality theorem to over here you have ÀNGEL, ABC and
let's have a line pick you over here such that BQ is parallel to B.C. If that is the case, then we
can conclude that the ratio of AP divided by B will be equal to the ratio of equal divided by QIC.
Let me write that over here, but this is the proportionality theorem, you take any triangle and if
you have this line parallel to this line and say this is X, this is why this is Z and this is W, and
as per the proportionality, you can state that X by, why is equal to that by W..
All right, let's move on.
The next theorem that we discuss is the Apollonius Theorem.
This is also a useful theorem to know.
Say you have a triangle, ABC over here.
Now let's construct a B over here.
That's that.
AP is the median.
That means BP is equal to peezy or is the midpoint of site B C, right.
We have discussed what we mean with the median now as per the Apollonius theorem, the sum of the squares
of A, B and AC will be equal to two times the sum of the squares of AP and either BP or ABC.
That's right, that over here A B squared plus X squared is equal to two times AP squared plus B square.
So for example, if this X and this is why this is that this is and this is it, then as per the Apollonius
theorem, X squared plus Y square will be equal to two times that squared plus a square.
Now these theorems are good to know.
You will get some questions and if you know these theorems ready at hand, you'll be able to solve them
very fast.