In this video, let's discuss why some of the properties that we discussed previously, also in the
case of a program.
All right, let's move ahead over here.
We take an example.
We have program ABCDE.
Remember, in a program opposite sides are equal and parallel to that means is parallel to city and
AC is parallel to Beatty.
And remember, Abe is equal to KDDI in length and AC is equal to beauty in length.
All right.
Now let's join Vertex C and Vertex B, so you get two triangles, you have Triangle HCB and Triangle
DBC So you have two triangles over here.
Now let's observe some interesting things about these two triangles.
You will see that angle.
BCB is equal to angle C B, so this angle over here, DCB is equal to angle S.B.
Now why is that so?
Because these are alternate interior angles, right.
You have a B parallel to Cirie and c.B is acting as the transversal.
And we know in this case, alternate interior angles are equal.
Similarly, you can see that Angle DBC is equal to Angle B.C. This angle over here is equal to this
angle over here.
Again, the reason is the same.
AC is parallel to beauty and c.B is acting as a transposon.
So alternating triangles are equal.
That's why these two angles are equal.
Now, KBE is equal to B.C. because it's a common sight.
So this is a common sight.
Now you can see when you observe these two triangles, you have two pairs of angles that are equal and
the included side is equal.
Therefore, Asper is a congruency.
We can say that triangle ABC is congruent to triangle DCB, right?
Remember, it has to be written in the correct way.
You have A, B, C over here.
Let's write ABC over here.
Let's have a triangle over here.
We know that angle ACB is equal to angle B, B, C, but over here is HCB.
So angle D, B.C. also should be over here, right?
That's why you have to over here.
You have B over here and you have see or hear.
These two angles are equal.
So they are put in the same position and you have angle A, B, C is equal to angle the C, so that's
also matching.
These two are equal.
Therefore Triangle ABC is congruently triangle DCB.
Now this is Asper a congruency.
Now let's move on.
We have proof that these two triangles are congruent and hence we can see that angle C is equal to angle
B, right.
What is Anglesey angle sees nothing but angle B, C, B plus angle ECB.
Right.
We have the ECB over here and we have A, C, B over here.
If I had these two together and if I had these two together, it would be the same.
Right.
So that's why we get here.
That Angle C is equal to angle B.
Similarly, you can prove that angle is equal to Angley.
That's why the opposite angles of a program are equal.
All right.
Let's see one more property, which we saw before.
We saw that the diagonals of a paragraph bisect each other.
Right now, let's try to understand why that is so over here we have a program, ABCDE.
Now, let me construct the two diagonals of this program.
I have AC and BD and let them intersect at point.
OK, all right.
Now let's take a triangle or a B and OKd.
OK, so this is all B and this is all C D right now, you will see that a B is equal to Katie.
Why is that so?
Because these are opposite sides of a battleground.
And we know that in a battleground, opposite sides are equal.
Anberlin so Abey's is equal to Kerry.
Now we know that these two angles are equal right angles the or is equal to Angle or B.
Why is that.
So these are already interior angles, right.
Because Abey's parallel to city and DBE is acting as a transversal.
Therefore these two angles are alternating angles and we have angle B always equal to angle Krio.
Similarly, we have angle DCO is equal to Angle or a C or a B.
Why is that so.
Because over here Abey's parallel to city and AC is acting as a transversal.
So again these two are alternate interior angles.
All right.
Now therefore triangle aob is congruently, triangle C or D astbury as a rule now because these two
triangles are congruent triangles, I can see that all is equal to or C and B is equal to Audy.
Right.
Or it will be equal to Ossy similarly.
Or B as to be equal to Audy because these are corresponding parts of two congruent triangles.
All right, so that's why we say that the diagonals in that program bisect each other that is always
equal to U.S. and Audie is equal to or B.