High students in this video, let's discuss similar triangles now, what are similar triangles to triangles,
which are of the same shape, but not necessarily of the same size?
These type of triangles are called similar triangles.
Let's take an example over here.
You can see that there are multiple triangles.
Now, all of these are similar.
That is Triangle A, B, C is similar to Triangle A, B three, C three is similar to Triangle A, B
to C two, etc..
Now, if you take two similar triangles, you will see that there are two interesting properties.
The first interesting property is that matching angles are equal and the next interesting property is
that the ratio of matching sides are the same.
Let's try to understand it using these triangles over here.
Now, over here we have seen triangle.
ABC is similar to Triangle A, B and C one.
That's this triangle over here.
And that is similar to Triangle E, B to C two.
And that is similar to triangulate B three, C three.
Right.
You can see that visually these four triangles are of the same shape, but they don't have the same
size.
All right.
Now, let's take any two for our study over here.
Let's take a triangle, ABC and Triangle A, B, two and C two.
In these two triangles, you can see that angle.
E is a common angle, right in A, B to C two.
Also, you have Angley and in ABC also you have angle it already and over here B to C two is parallel
to B C, therefore these two angles are equal because they are corresponding angles right over here.
This line is parallel to this line and B to be is acting as the transversal.
Therefore, this angle over here and this angle over here are corresponding angles and they are equal.
Similarly, angle AC to be two is equal to Angle ACB, right.
Again, because we to see two is parallel to B.C. and over here see to see this line over here is acting
as the transverse.
Therefore these angles are also corresponding angles and hence they are equal.
All right.
So we have seen this part over here.
Imagine the angles are equal in Triangle ABC and Triangle B to NC.
To the second property over here is that the ratio of matching sites are the same.
What does that mean?
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.
Right.
You have a B over here, that's this side and a B to that's the side.
So these are matching sides.
This ratio will be equal to the ratio between B, C and B to C two.
All right.
So these two sides also will have the same ratio and that ratio will be equal to AC divided by a C two,
because these are the ratio of matching sites.