In this video, let's discuss another important type of collateral that is a foresighted polygon.
All right.
What is a kite?
A kite is a figure like this.
Over here, you have two sets of a decent size being equal.
That is this side is equal to this side and this side is equal to decide.
This is also a kite over here.
And you can see these two sides are equal and these two sides are equal.
This type of a shape is what we call a kite.
That is two sets of consecutive sides are of equal length.
All right.
Now, let me name these vertices as A, B, C and D.
Now let's discuss the other properties of A quite annoying.
These properties can save you a huge amount of time in solving a lot of difficult questions.
So let's proceed in a kite.
You will have one set of opposite angles, equal or here and will be is equal to.
And you'll see and remember, it will be the angle formed by the non equal sides and will be is formed
by ABC, NBC and these two sides are not equal.
Right.
Similarly Angle D form by Eddie and DC and these two sides are not equal.
So indicate the angles formed by the non equal sides will be equal.
All right, let's proceed.
Let me join ANC and be Andy, so I get the diagonals over here right now indicate you will see that
the diagonals intersect at 90 degrees.
So these angles are all equal to 90 degrees.
All right, let's proceed.
What is another interesting property about Caite?
You will find that the longer diagonal bisects the shorter diagonal or here it is, the longer diagonal.
Right.
And this one will bisect beedi, which is the shorter diagonal.
That means this side on this side are equal.
If I call this point of intersection as all, then I can see that we or is equal to Audy.
All right.
Now what is one more interesting property?
The longer diagonal is the angle bisected.
That means these two angles are equal and these two angles are equal.
Let me mark the mass angle.
One, two, three and four.
Angle one is equal to angle to an angle.
Three is equal to angle, for these are all the important properties about right now.
Let's try to think logically why this is so over here.
We have that this side is equal to this site.
This side is equal to the center right.
So let's analyze triangle A, B, B and triangle A, B, C.
If you see these two triangles, you will see that AB is equal to eighty because equal to an AC is a
common sight.
So these two triangles are congruent.
Asper assesses congruence criteria now because this triangle over here and this triangle over here,
these two are congruent.
Therefore we can say that corresponding angles are equal, right?
That's right.
And will be equal only because these two angles are corresponding angles right now.
Also, we can see that.
Angle one is equal to angle two and three is equal to and therefore because of the same reason, these
are also corresponding angles of these two congruent triangles.
So we have seen why this is so and we have seen why the longer diagonal is the angle by sector.
Now let's see why the other properties are.
So if you take a triangle, HBO, let me right over here.
And if you take triangulator you.
You will see that these two are also congruent.
Why is that so we have angle one angle to it.
We have proved it over here and we have abs equal to 80.
And it is a common sight.
Therefore, Asper, this is congruence criteria.
These two triangles are also congruent.
That's why we all is equal to Odey.
So the longer diagonal bisects the shorter diagonal, we have seen why this is so and angle it or B
will be equal to angle like that over here and it will be will be equal to angle E or B because the
corresponding angles of two congruent triangles.
Now these two triangles also form a linear right because this is a straight angle, therefore they are
equal and some of them is equal to 180 degrees.
Therefore, each of them is equal to 90 degrees.
That's why this property over here is true.
That is, the diagonals intersect at ninety degrees.
So let's quickly summarize.
We have seen some very interesting properties about Kite's and we have seen why they are so using congruency
of triangles already to indicate there are two sets of consecutive equal sides.
Right.
That's property one.
We have seen that the diagonals intersect at 90 degrees.
The longer diagonal bisects, the shorter diagonal and the longer diagonal is the angle by sector.
We have also seen that there is one pair of opposite angles which are equal and these angles are formed
by a set of non equal sites.
That is Angle B is formed by ABC and these two are not equal.
Similarly, Angle is formed by Eddie and DC and these two are not equal.