Students in this video, let's discuss about squares now, what is the square?
The square is a shape like this where you have every side equal.
So this is equal to a this is equal to this is equal to it.
And this is equal to it.
And each of these angles is equal to 90 degrees.
And you will see that these two sides are parallel to each other and these two sides are parallel to
each other.
This type of a shape is what we call a square.
Now, a square is a rectangle with equal sides.
So every square is a rectangle, but a rectangle is not square.
Right.
So what is a rectangle?
We have seen that a rectangle is a shape like this where every angle is 90 degrees and opposite sides
are parallel and equal.
Right.
So if this is a this is it.
If this is B, this is B, you can see that A square is a special type of rectangle where these sides
are all equal.
All right, let's press on.
So we have seen what we mean with the square and we have seen that it's a rectangle with equal sides.
All right.
Now, in a rectangle, the diagonals are equal, right?
We have already discussed that.
Therefore, in a square also, the diagonals are equal.
All right.
Now, there is an additional thing that we can understand when we are dealing with the square, and
that is that the diagonals are perpendicular bicyclers of each other in the case of a rectangle.
We have seen that the diagonals are bicyclers of each other and the diagonals are equal.
Right.
In the case of a parlor game itself, the diagonals are bicyclers of each other.
Now, in the case of a square, the diagonals are equal and they are perpendicular sectors of each other.
Let's try to understand this very important property over here.
I have square ABCDE.
Now let the length of the side of the square, be it.
Now let's quickly take a side note and discuss what would be the area and perimeter of the square.
The area would be into it and the perimeter for it.
Right.
Because this, this and this side is also equal to it.
That's where the perimeter is for it.
And the area of a rectangle is side to side.
Right.
So over here, all the sides are.
That's why it's into it, which is a square.
All right.
Now let's come back to diagnose of a square.
Let me construct the diagonals of this square, ABCDE.
That's easy and beauty.
All right.
Now, let them intersect at point all over here.
Now let's see that triangle E or D, that is this triangle over here is congruently triangle A or B.
Let's prove that that's Asper as rule.
Why is that so?
It is a common sight.
Right.
And it is equal to B because each side of the square is equal to eight and you will see that already
is equal to orby because the diagonals bisect each other in the case of a rectangle and we have seen
that square is a special type of rectangle.
So as far as this rule, these two triangles are congruent with each other.
Therefore, I can say that this angle over here and this angle over here that is angle awadi is equal
to angle.
It will be because they are corresponding angles of these two congruent triangles.
Also, we can see from the diagram that angle awadi plus angle it will be is equal to 180 degree because
they form a straight angle or these two angles, former linear pair.
Therefore putting these two things together, we can find that angle awadi is equal to angle.
It will be that's equal to 90 degrees.
So these two angles are 90 degrees and that's why we say that diagonals of a square are perpendicular
bicyclers of each other.