Students in this video, let's discuss the as a rule to test congruency of two triangles, say we have
a triangle ABC over here and let's say we have one more triangle over here.
Let me name it as Triangle Park.
You are.
All right, now, Asper, this rule, if I have two sets of angles that are equal to the angle, be
an angle.
Q are equal and angle C and angle are equal.
And if the included side is equal, so B C is equal to cure, then I can say that these two triangles
are congruent.
That's what this rule says.
All right.
Now let's try to understand it better over here.
We are given two angles and one side right now.
This rule is a valid rule to test congruency.
If I can draw an exact copy of Triangle ABC without any ambiguity with just these three pieces of information.
Let's take B.C., for example, has five centimeter led angle B B hundred degrees and let Anglesey four
degrees.
Now let's check whether, given only these three pieces of information, whether I can draw a copy of
this triangle or not.
All right.
Let's start with constructing P Q, which is equal to five centimeter.
That's just a line segment.
Now at Q Let me draw an angle equal to 40 degree.
So that would look like this now at P.
Let me draw an angle which is equal to 100 degrees and you will see that they intersect at this point.
Let me call this point as point R and you can see that we have got Triangle R, B, Q, which is an
exact copy of Triangle ABC.
Therefore, A.S.A. is a valid rule to check congruency of two triangles.
Now what is it that this rule says?
If two angles and the included side of a triangle are equal to the corresponding angles and included
side of another triangle, then the two triangles are congruent.
Now you will see that in some textbooks you will also have a rule called A-S, which is angle, angle
and any side.
The difference between these two is over here.
This is about the included side, right?
That's what we have mentioned over here.
It's the included side.
But over here, it just means any side.
Now, these two rules are actually one and the same.
Why is that?
So let's say that two angles are equal.
That's angle B, an angle B are equal to angle is 100 degrees angle CNN.
You are equal.
Let this be 40 degrees now.
And it's given that this side and this side is equal right now or here.
If two angles are equal, then definitely the third angle also will be equal, right.
What would be angle over here?
It's 180 minus one hundred minus 40, which is 40 degrees.
Similarly, you will see that angle out over here is 180 minus hundred minus 40, which is equal to
40.
So if two angles are equal, definitely the third set of angles are also equal among the two triangles.
So if to start with, you are given that angle is an angle, we are respectively equal to angle or an
angle B and you are given that B C is equal to BQ, right.
Then you can change that to SC by just finding that the third angle also will be equal and this just
becomes equal.
And two is it, is it.
And it's it's almost one and the same.