Students, let's discuss isosceles triangles in greater detail in this video, we have already seen
that an isosceles triangle is a triangle whose two sides are equal.
So let me call side Ebb's X and side Acee as X.
So these are of length X, say centimetre and side because of lengthwise centimeter.
Now, this is an example of an isosceles triangle.
We have also seen that the angles opposite the equal sides are equal.
So in this case, Angle B is equal to angle C or we can see Angle ABC is equal to Angle HCB.
All right.
Now let's move on and understand some more interesting things about the isosceles triangle.
Let me draw a B over here such that a B is the order of angle it.
So is the angle by sector of angle.
That means this angle over here is equal to this angle over here.
Now, if that is true, then you will see that IPE is also the perpendicular by sector of B.C. and you
will see that B is the median to B.C..
Now let's see why that is.
So over here you can see that triangle EPB is congruent to triangle ABC.
That's this triangle A, B, B is congruent to triangle A, B, C, and you tell me why that is.
So it's Asper as it is congruence criteria Y EP is equal to Eppy.
That's a common sight.
A B is equal to AC y because it's an isosceles triangle and it's given that these two sides are equal
and and be a particular angle.
C AP that's BNP is equal to Capri.
Why is that.
So it's Aspell construction.
Right.
AP is the angle by sector of angle.
Therefore these two triangles are congruent and that gives us that this side let me call it a b b b
B is equal to b c.
Why.
Because they are corresponding sites of congruent triangles.
Similarly, you can see that this angle over here is equal to this angle.
And let me try that over here.
Angle EPB.
Is equal to angle E, B, C, right, and they also are forming a linear pair, therefore angle B,
B, plus angle ABC is equal to 180 degree because they are equal and there is equal to 180 degrees.
So each of them has to be 90 degree to these two things together.
Gives us that.
AP is the perpendicular by sector of B.C., similarly, because BP is equal to B.C., we get that A
B is the median to B.C..
All right.
Now, there's one more interesting thing you can note, because triangle A, B, B is congruently triangle
ABC.
Therefore, this area over here will be equal to this area over here.
Therefore, this line that is AP is dividing triangle ABC into two parts of equal area.
All right, so these are some interesting things that we have observed about isosceles triangles.