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High students in this video, let's discuss similar triangles now, what are similar triangles to triangles,

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which are of the same shape, but not necessarily of the same size?

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These type of triangles are called similar triangles.

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Let's take an example over here.

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You can see that there are multiple triangles.

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Now, all of these are similar.

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That is Triangle A, B, C is similar to Triangle A, B three, C three is similar to Triangle A, B

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to C two, etc..

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Now, if you take two similar triangles, you will see that there are two interesting properties.

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The first interesting property is that matching angles are equal and the next interesting property is

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that the ratio of matching sides are the same.

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Let's try to understand it using these triangles over here.

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Now, over here we have seen triangle.

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ABC is similar to Triangle A, B and C one.

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That's this triangle over here.

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And that is similar to Triangle E, B to C two.

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And that is similar to triangulate B three, C three.

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Right.

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You can see that visually these four triangles are of the same shape, but they don't have the same

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size.

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All right.

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Now, let's take any two for our study over here.

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Let's take a triangle, ABC and Triangle A, B, two and C two.

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In these two triangles, you can see that angle.

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E is a common angle, right in A, B to C two.

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Also, you have Angley and in ABC also you have angle it already and over here B to C two is parallel

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to B C, therefore these two angles are equal because they are corresponding angles right over here.

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This line is parallel to this line and B to be is acting as the transversal.

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Therefore, this angle over here and this angle over here are corresponding angles and they are equal.

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Similarly, angle AC to be two is equal to Angle ACB, right.

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Again, because we to see two is parallel to B.C. and over here see to see this line over here is acting

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as the transverse.

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Therefore these angles are also corresponding angles and hence they are equal.

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All right.

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So we have seen this part over here.

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Imagine the angles are equal in Triangle ABC and Triangle B to NC.

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To the second property over here is that the ratio of matching sites are the same.

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What does that mean?

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A B divided by a B two will be equal to B, C by B to C two and that will be equal to AC by E, C two.

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Right.

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You have a B over here, that's this side and a B to that's the side.

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So these are matching sides.

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This ratio will be equal to the ratio between B, C and B to C two.

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All right.

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So these two sides also will have the same ratio and that ratio will be equal to AC divided by a C two,

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because these are the ratio of matching sites.