In this video, let's continue learning properties about Sakalys, we have so far seen that if you have
an ark and it's obtaining an angle over here, that's Angle EPB, then Angle APB will be equal to half
of the measure of the arc.
That's angle.
It will be.
All right.
Let's continue learning some interesting properties.
Let me take one more point over here and subtrend one more angle.
So this is angle A you be right now, the property says that the angle SUB-STANDARD by the same arc
are equal right now.
Over here, that means angle EPB is equal to angle accuracy and we can understand why that is.
So we have seen Angle EBP is equal to half of Angle Elby angle.
A cube also will be equal to half of angle.
It will be.
Now, because these two are equal, these two also will be equal.
That's right.
Angle EPB is equal to angle A.
All right.
But that's an interesting property that we have learned over here.
Let's continue learning one more interesting property in this video.
So I have a circle over here now.
I have to ask, this is Abe and Arc B are now over here.
Let me draw the measure of Archabbey and the measure of Arc B are now the property says that if Angle
eight will be that's this angle over here is equal to angle B or that's this angle over here, then
the cord maybe that's this court will be equal to the court b r and remember the court is the straight
line joining two points.
So if angle A or B is equal to angle B or then A, B will be equal to P R and the reverse is also true.
That is if angle if Mr AB is equal to measure B, that is the length Abe is equal to PR then this and
Gloria that's angle A or B will be equal to and group B or.
All right.
So that's, that's a very interesting property.
Let's quickly think why that is so, so that that will help you retain this new information.
All right.
Now we know that or A or B or B and or are already eight.
Right.
So these are all equal.
Now, let's try to analyze triangle A or B and triangle B or.
You can see that all is equal to or B because they are really similarly or is equal to or they are also
radiate right now, say it is given that angle Elby is equal to pure.
So then we have one set of included angles are equal.
Therefore these two triangles are congruent Asper s se congruency criteria and hence we can say that
AB is equal loopier.
Right?
So that's this weight of the relation.
Now, the opposite way also would be true.
We know that these two sets of sides are equal.
If it's given that ABS equal appear, then we have three sets of sides equal.
Therefore, as parentheses rule, we can find that these two triangles are congruent and in that case,
angle aob will be, will be equal to and will be lower because they are corresponding angles of two
congruent triangles.
Alright, let's summarize.
We have seen that if angle aob is equal to angle B or then it is equal to PR and we have seen that this
is true because of S.A.S. and if is equal loopier that's given, then angle it will be will be equal.
Rupia are because of this congruence criteria.
All right.
But that's also very interesting.
Property of triangles.
Let's see one more interesting property in the next video.