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In this video, let's discuss an interesting property about triangles, the property states that the

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sum of any two sides of the triangle will be greater than the third side.

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For example, if you are A, B and B, C, that has to be greater than Issie, which is the third side.

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Now, we can also think of it in this way.

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Imagine is a city and sees a city.

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Now, you could travel from a to see in two ways along parts of the triangle.

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Right.

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You can travel in this way or you can travel from A to B and then from B to C.

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Now this part over here will be shorter than traveling from A to B and then from B to C.

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Let's try to think a little bit deeper about this.

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Over here.

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We have a particular triangle right now.

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Let's increase AC by increasing its land.

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So that would somewhat look like this, right?

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So it is now bigger than what is he was over here.

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Now, over here we see less than A, B plus B, C, right.

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So that's why we are increasing the AC.

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That's again in Greece.

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Is he the diagram becomes like this.

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Now, if you increase more, that's that AC is equal to A, B plus B, C right over here is less than

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A, B plus B, C, if you increase it such that AB is equal to A, B plus B, C, it will look like

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this.

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Right.

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So AB plus B.C. is equal to AC, so it does not form a triangle, it's forming a straight line.

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So if you have a triangle, definitely the sum of two sides of the triangle will be greater than the

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third side.

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All right, let's press on let's ride this over here.

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Some of two sides of a triangle is greater than the third side.

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Now, let's derive one more property on the basis of this property, which we have seen, the difference

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of two sides of a triangle will be less then the third side.

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Now, let's model the length of the sides of this triangle as A, B and C, the length of the side,

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which is opposite angle is taken as smaller three and similarly smaller to B is opposite angle B and

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C is opposite angle.

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See.

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All right.

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Now I split this property over here.

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We know that A plus B will be greater than C right now.

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If I take B to the right hand side, you can see that you get C minus B is less than A, right.

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You can write it as it is greater than C minus B, and that's the same as writing A, C minus B is less

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than eight.

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And that's what we have said over here.

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The difference of two sides of a triangle will be less than the third side.

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All right, let's take these two properties over here.

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Now, see, you are given two sides of a triangle as five and twelve.

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So two sides are given.

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One side is five and one side is twelve centimetres.

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Now, what are all the possible values that the third side can take?

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The third side will be greater than twelve minus five and the third side will be less than twelve plus

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five.

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That is twelve minus five gives you seven to seven less than the third side.

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Less than one plus five gives you seventeen.

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So if it is given that the third side, for example, is six centimetre, then five, twelve and six

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cannot form a triangle, or if it's given that the third side is eighteen centimetre, then five, 12

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and 18 cannot form a triangle.

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So the third side can only take values in between five and 17.

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And remember, it's not including 17 and seven to seven and 17 also can not be the third side.

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The values, the integral values that are possible for the third side are eight, nine, ten, eleven.

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Up to sixteen.