In this video, let's discuss two things that is a common mistake among students.
Now we have learned four methods to check on currency of two given triangles.
What were they?
We saw the Essence's rule.
We saw the SARS rule.
The NCAA rule or a rule, right?
E is.
And we've seen the arches rule.
These are the four rules that we discussed.
Now, E or S.
S e these two are not rules to check congruency.
So let's try to understand why they are not sufficient rules to establish congruency of two triangles.
All right.
Now, let's start with a think of a smaller and bigger equilateral triangle.
We know that in an equilateral triangle, all the angles are equal to 60 degrees.
Right.
Let me take two equilateral triangles over here.
I have a small triangle and a bigger equilateral triangle.
Let's say that the side over here is two centimeter and let the side over here be 10 centimeter.
Now, because all the angles are equal to 60 degrees, I can say that this angle is equal to this angle.
Right.
I can say at this angle is equal to this angle.
And I can see this angle is equal to this angle.
Right.
But it's clearly visually evident that these two triangles are not congruent.
If you superimpose this triangle on top of this triangle, it will not cover exactly right.
Therefore, these two triangles are not congruent and hence it is not sufficient to establish congruency
of two triangles.
All right.
Now, let's move on to S.
S e now as it means you have two sides given and you have given an angle, which is not an included
angle.
Right.
Let's take an example.
Let me have a triangle over here.
Let's say this is Triangle ABC and we know this side.
We know this site and we are given this angle right now, can you draw a triangle with only these three
pieces of information without any ambiguity?
No, you cannot, right.
Why is that so?
Because two triangles are possible with these three conditions satisfied.
Let's see them.
You have two triangles over here.
These two triangles satisfy the given criteria.
That is B-R is equal to argue is equal to Acey and this angle Q is equal to this angle C right now.
Instead of constructing it over here, I could take it like this also.
Right.
But what's happening over here is you start constructing BQ, that's step one.
And then at point.
Q which is any point because you don't know this length.
So this is just a line.
You draw a line from point Q at an angle equal to the different angle C over here.
So you get a construction like this.
We have drawn a line like this and you draw a line like this at the given angle.
So this angle is equal to Anglesey over here.
Now we know this length.
So let me measure out this length and find a point over here.
Let me take that point.
This point are right now, we have used up two pieces of information.
The third piece of information that we have is we know the length of a B.
All right.
Now, I have this line segment going on like this now with my compass.
Let me put the sharp edge at point out and let me draw an arc.
You will see that in many cases it will intersect this line in two points.
So you can construct B are like this, which is case one, which is this case over here.
Or you can construct we are like this.
Right, which is this case over here.
So you are not able to construct an exact copy of Triangle ABC when you just have two sides and an angle,
which is not the included angle given there is ambiguity without ambiguity, you're not able to construct
a copy of Triangle ABC.
Hence SC is not a sufficient condition to establish congruency of two triangles.
Right?
Again, you can see why that is.
So say you have this triangle over here and you have this triangle over here, which we can see that
if you superimpose one on top of the other, it will not cover it exactly right.
And hence SSA is not a sufficient condition to establish congruency.