In this video, let's discuss the exterior angle property of a triangle.
This is a very important property.
We start in a very easy manner so that your fundamentals are rock solid and then we progress to more
difficult questions.
All right.
Let's take an example.
We have Triangle ABC over here.
Let's extend ABC in this way and let's mark a point over here.
All right.
Now, this angle over here, which is angle asid, is an exterior angle of triangle ABC at Vertex Seat.
So at this vertex, we have formed an exterior angle by extending one of the sides.
Right.
So we extend ABC and we got this angle.
And this type of an angle is called an exterior angle.
All right.
This type of an angle has an interesting property.
Before we go ahead with that, let's discuss what the other angles over here are.
You can see that ACD is adjacent to HCB, right.
So this angle over here is adjacent to this angle.
The other two angles are these angles, which is angle and angle B and these remaining angles.
That is the angles which are not adjacent to the exterior angle are called interior opposite angles.
You can see that they're interior to the triangle.
Right.
And they are opposite to this angle over here.
Or you can think of it as opposite to the angle which is adjacent to the exterior angle.
So they are not adjacent to it.
All right.
Now, having established the basic terminology, let's move ahead.
As per the exterior angle, property angle, A.D. will be equal to angle a plus angle beat, and that's
what we call the exterior angle property of a triangle that is the exterior angle is equal to the sum
of the interior opposite angles.
And we have seen that angle and we are the interior opposite angles.
Now let's see why this is true.
Let's construct a parallel line at sea, which is parallel to be so able to see right now.
Over here, you can see that.
E C is splitting angle ACD into two, let's mark this angler's angle way and let this be angle X.
Now angle X will be equal to angle E because there are alternate interior angles right over here.
Abes parallel to easy and X acting as a transposon.
Remember, we had seen that when two lines are intersected by a transpersonal, the alternate interior
angles are equal.
So using this property over here, we see that angle X is equal to angle a similarly angle Y is equal
to angle B because they are corresponding angles, right?
Abes parallel to E, C and B is acting as the transversal.
Therefore, this angle over here and this angle over here are corresponding angles right over here.
Remember when two lines are parallel and there intersected by a transversal angle, one angle five are
corresponding angles.
Right.
It's the same scenario over here.
We have a parallel to see and beardie is the transposon.
Therefore angle Y is equal to angle B.
Now we know that angle ACDA is equal to angle X plus angle Y, right.
You can see that from the figure angle ACD is equal to X plus white and X is equal to Angley.
And why is equal angle B therefore we can write it as angle actis equal to angle A plus angle B or the
exterior angle is equal to the sum of the interior opposite angles.
Now we could have also proved this in another way.
We will soon learn the interior angle, some property of a triangle.
That is, if you add the three angles of a triangle, you will get 180 degrees.
Now using that also we could have brooded.
For example, you can see angle eight plus angle B plus angle B, C.
Has to be 180 degrees and we will soon see that why this is so and angry A.D., which is the extent
angle plus angle ACB.
Also is equal to 180 degrees.
Why is that so?
Because these two former Leanyer pair now by equating these two, we can cancel off BSEE from here and
here.
And again, you will get Anglicised is equal to Angley plus angle B, so let's summarize the triangle
property of a triangle says that the exterior angle over here we have taken 160 exterior is equal to
the sum of the interior opposite angles.