In this video, let's discuss the Essence's criteria to check whether two given triangles are congruent
or not.
All right, let's start with this.
Your given triangle, ABC, and you're asked to draw a copy of it.
All right.
So this is Triangle ABC, and whoever is telling you to draw a copy tells you that side AC is seven
centimetre side, ABC is six in the middle and side B, C is five centimeter.
Is this information sufficient to draw a copy of ABC without any ambiguity?
Let's try it.
Let's make a statement, if you know the three sides of the triangle, you can draw a copy.
All right, let's experiment whether this is true, but I have BCS equal to five centimeter.
So let me draw a line because you sense that it's a five centimetre length.
All right.
Now, it's given that a B is of six centimetre, right?
It's six centimeter.
So let me take my compass, put the sharp edge at point B and draw and are such that the radius of the
compass is six centimeter.
All right.
Now, similarly, let me take my compass or the sharp edge at point.
Q And draw an arc over here such that it cuts the previous arc and let the radius of the compass at
this time be seven centimeter.
So I do it over here like this.
Now these two arcs intersect at that point.
Let me join that point with Q and B, do I do that like this?
And similarly I do that over here.
All right.
Now, let me mark this point, as are you can see that if I have three sides of a triangle, I can draw
a copy of it without any ambiguity.
This is what we call the essence's criteria of congruence.
Let's quickly repeat it.
If you are given the three sides of a triangle, you can draw a copy of it.
And there is no ambiguity.
That is, there is only one shape in the form of a triangle where the three sides will be as per the
given length.
There won't be a case where you can draw two triangles, two different triangles, such that the three
sides are as part of the given length.
Therefore, if you know that the three sides of a triangle are equal to the corresponding three sides
of another triangle, then they are congruent.
Let's take an example over here you have triangle and here you have another triangle.
Say it's given that this side is five centimetre, this is six centimetre and this is four centimetre
and C for this triangle, it's given that this side is six centimetre, this is five centimetre and
this is all centimetre then because there are two sides which are equal.
So this side is equal to decide.
This side is equal to this side and this side is equal to this side.
So there are three sides are equal to corresponding three sides.
Therefore, we can conclude that these two triangles are congruent.