In this video, let's learn how can we establish whether two given triangles are similar or not?
Now, there are two rules which we can use to establish whether two triangles are similar.
That's the a rule and the is rule.
Now, this says rule is different from the test for congruency.
Let's eat.
Let's start with the rule or here.
This rule states that if two angles of a triangle are equal to two angles of another triangle, then
the two triangles are similar.
Let's try to understand it.
Over here we have two triangles.
Let this angle be equal to this angle and let this angle be equal to this angle.
So there are two sets of equal angles.
Therefore, as per the error rule, these two triangles are similar.
That is, these two triangles will have the same shape, but not necessarily the same size.
All right.
Now let's move on to the SARS rule.
The SARS rule states that if two ratios of corresponding sides are equal and the included angles are
equal, then the two triangles are similar.
All right.
So there are two criteria over here, two ratios of corresponding sites.
That's what this is and this stands for.
So over here, this stands for ratio of corresponding sites.
And this is also stands for ratio of corresponding sites and this is stands for the included angle.
And that one has to be equal.
All right.
Let's try to understand it with an example.
Let me Marty, vertices of these triangles as ABC and BQ are now over here.
Let's take two corresponding sides to be equal.
That is A, B divided by P, Q, right.
This ratio should be equal to let's take a C divided by P, R and B include an angle over here between
this site and decide exactly.
And the included angle between this site and this site is angle P.
So the criteria is everybody p q is equal to AC by fiat that stands for the two is right and angle is
equal to angle B.
That's the included angle has to be equal between these sites.
Now if that is true, then we can see that triangle.
ABC is similar to triangle pick you up.
So let's quickly revise.
We have learned to criteria's which we can use to check whether two given triangles are similar or not.