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In this video, let's discuss another important type of collateral that is a foresighted polygon.

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All right.

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All right.

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What is a kite?

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A kite is a figure like this.

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Over here, you have two sets of a decent size being equal.

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That is this side is equal to this side and this side is equal to decide.

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This is also a kite over here.

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And you can see these two sides are equal and these two sides are equal.

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This type of a shape is what we call a kite.

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That is two sets of consecutive sides are of equal length.

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All right.

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Now, let me name these vertices as A, B, C and D.

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Now let's discuss the other properties of A quite annoying.

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These properties can save you a huge amount of time in solving a lot of difficult questions.

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So let's proceed in a kite.

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You will have one set of opposite angles, equal or here and will be is equal to.

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And you'll see and remember, it will be the angle formed by the non equal sides and will be is formed

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by ABC, NBC and these two sides are not equal.

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Right.

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Similarly Angle D form by Eddie and DC and these two sides are not equal.

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So indicate the angles formed by the non equal sides will be equal.

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All right, let's proceed.

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Let me join ANC and be Andy, so I get the diagonals over here right now indicate you will see that

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the diagonals intersect at 90 degrees.

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So these angles are all equal to 90 degrees.

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All right, let's proceed.

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What is another interesting property about Caite?

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You will find that the longer diagonal bisects the shorter diagonal or here it is, the longer diagonal.

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Right.

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And this one will bisect beedi, which is the shorter diagonal.

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That means this side on this side are equal.

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If I call this point of intersection as all, then I can see that we or is equal to Audy.

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All right.

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Now what is one more interesting property?

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The longer diagonal is the angle bisected.

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That means these two angles are equal and these two angles are equal.

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Let me mark the mass angle.

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One, two, three and four.

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Angle one is equal to angle to an angle.

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Three is equal to angle, for these are all the important properties about right now.

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Let's try to think logically why this is so over here.

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We have that this side is equal to this site.

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This side is equal to the center right.

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So let's analyze triangle A, B, B and triangle A, B, C.

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If you see these two triangles, you will see that AB is equal to eighty because equal to an AC is a

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common sight.

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So these two triangles are congruent.

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Asper assesses congruence criteria now because this triangle over here and this triangle over here,

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these two are congruent.

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Therefore we can say that corresponding angles are equal, right?

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That's right.

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And will be equal only because these two angles are corresponding angles right now.

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Also, we can see that.

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Angle one is equal to angle two and three is equal to and therefore because of the same reason, these

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are also corresponding angles of these two congruent triangles.

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So we have seen why this is so and we have seen why the longer diagonal is the angle by sector.

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Now let's see why the other properties are.

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So if you take a triangle, HBO, let me right over here.

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And if you take triangulator you.

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You will see that these two are also congruent.

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Why is that so we have angle one angle to it.

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We have proved it over here and we have abs equal to 80.

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And it is a common sight.

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Therefore, Asper, this is congruence criteria.

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These two triangles are also congruent.

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That's why we all is equal to Odey.

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So the longer diagonal bisects the shorter diagonal, we have seen why this is so and angle it or B

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will be equal to angle like that over here and it will be will be equal to angle E or B because the

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corresponding angles of two congruent triangles.

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Now these two triangles also form a linear right because this is a straight angle, therefore they are

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equal and some of them is equal to 180 degrees.

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Therefore, each of them is equal to 90 degrees.

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That's why this property over here is true.

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That is, the diagonals intersect at ninety degrees.

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So let's quickly summarize.

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We have seen some very interesting properties about Kite's and we have seen why they are so using congruency

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of triangles already to indicate there are two sets of consecutive equal sides.

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Right.

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That's property one.

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We have seen that the diagonals intersect at 90 degrees.

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The longer diagonal bisects, the shorter diagonal and the longer diagonal is the angle by sector.

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We have also seen that there is one pair of opposite angles which are equal and these angles are formed

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by a set of non equal sites.

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That is Angle B is formed by ABC and these two are not equal.

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Similarly, Angle is formed by Eddie and DC and these two are not equal.