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In this video, let's discuss two things that is a common mistake among students.

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Now we have learned four methods to check on currency of two given triangles.

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What were they?

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We saw the Essence's rule.

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We saw the SARS rule.

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The NCAA rule or a rule, right?

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E is.

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And we've seen the arches rule.

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These are the four rules that we discussed.

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Now, E or S.

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S e these two are not rules to check congruency.

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So let's try to understand why they are not sufficient rules to establish congruency of two triangles.

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All right.

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Now, let's start with a think of a smaller and bigger equilateral triangle.

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We know that in an equilateral triangle, all the angles are equal to 60 degrees.

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Right.

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Let me take two equilateral triangles over here.

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I have a small triangle and a bigger equilateral triangle.

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Let's say that the side over here is two centimeter and let the side over here be 10 centimeter.

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Now, because all the angles are equal to 60 degrees, I can say that this angle is equal to this angle.

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Right.

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I can say at this angle is equal to this angle.

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And I can see this angle is equal to this angle.

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Right.

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But it's clearly visually evident that these two triangles are not congruent.

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If you superimpose this triangle on top of this triangle, it will not cover exactly right.

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Therefore, these two triangles are not congruent and hence it is not sufficient to establish congruency

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of two triangles.

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All right.

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Now, let's move on to S.

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S e now as it means you have two sides given and you have given an angle, which is not an included

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angle.

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Right.

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Let's take an example.

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Let me have a triangle over here.

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Let's say this is Triangle ABC and we know this side.

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We know this site and we are given this angle right now, can you draw a triangle with only these three

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pieces of information without any ambiguity?

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No, you cannot, right.

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Why is that so?

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Because two triangles are possible with these three conditions satisfied.

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Let's see them.

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You have two triangles over here.

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These two triangles satisfy the given criteria.

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That is B-R is equal to argue is equal to Acey and this angle Q is equal to this angle C right now.

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Instead of constructing it over here, I could take it like this also.

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Right.

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But what's happening over here is you start constructing BQ, that's step one.

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And then at point.

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Q which is any point because you don't know this length.

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So this is just a line.

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You draw a line from point Q at an angle equal to the different angle C over here.

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So you get a construction like this.

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We have drawn a line like this and you draw a line like this at the given angle.

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So this angle is equal to Anglesey over here.

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Now we know this length.

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So let me measure out this length and find a point over here.

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Let me take that point.

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This point are right now, we have used up two pieces of information.

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The third piece of information that we have is we know the length of a B.

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All right.

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Now, I have this line segment going on like this now with my compass.

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Let me put the sharp edge at point out and let me draw an arc.

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You will see that in many cases it will intersect this line in two points.

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So you can construct B are like this, which is case one, which is this case over here.

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Or you can construct we are like this.

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Right, which is this case over here.

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So you are not able to construct an exact copy of Triangle ABC when you just have two sides and an angle,

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which is not the included angle given there is ambiguity without ambiguity, you're not able to construct

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a copy of Triangle ABC.

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Hence SC is not a sufficient condition to establish congruency of two triangles.

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Right?

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Again, you can see why that is.

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So say you have this triangle over here and you have this triangle over here, which we can see that

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if you superimpose one on top of the other, it will not cover it exactly right.

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And hence SSA is not a sufficient condition to establish congruency.