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In this video, let's discuss the midpoint theorem, this is quite a useful theorem in many questions.

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Now, over here you have a triangle, ABC.

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Now let's join the midpoints of ABC and AC.

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Let me be the midpoint of ABC and to be the midpoint of AC.

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All right, so we have joined the midpoint of Ebbe and Acey, right, because PE's the midpoint of a

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particular Beeby and because Q is the midpoint of Acee, AQ is a galaxy now as per the midpoint theorem.

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If this is the case, then P Q will be parallel to B C that's one result.

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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

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length of B, C will be to A.

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All right, so over here, we have got two interesting results using the midpoint theorem, let's learn

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a few more interesting properties on triangles.

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The next theorem that we discuss is the proportionality theorem to over here you have ÀNGEL, ABC and

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let's have a line pick you over here such that BQ is parallel to B.C. If that is the case, then we

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can conclude that the ratio of AP divided by B will be equal to the ratio of equal divided by QIC.

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Let me write that over here, but this is the proportionality theorem, you take any triangle and if

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you have this line parallel to this line and say this is X, this is why this is Z and this is W, and

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as per the proportionality, you can state that X by, why is equal to that by W..

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All right, let's move on.

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The next theorem that we discuss is the Apollonius Theorem.

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This is also a useful theorem to know.

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Say you have a triangle, ABC over here.

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Now let's construct a B over here.

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That's that.

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AP is the median.

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That means BP is equal to peezy or is the midpoint of site B C, right.

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We have discussed what we mean with the median now as per the Apollonius theorem, the sum of the squares

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of A, B and AC will be equal to two times the sum of the squares of AP and either BP or ABC.

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That's right, that over here A B squared plus X squared is equal to two times AP squared plus B square.

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So for example, if this X and this is why this is that this is and this is it, then as per the Apollonius

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theorem, X squared plus Y square will be equal to two times that squared plus a square.

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Now these theorems are good to know.

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You will get some questions and if you know these theorems ready at hand, you'll be able to solve them

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very fast.