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In this video, let's discuss why some of the properties that we discussed previously, also in the

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case of a program.

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All right, let's move ahead over here.

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We take an example.

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We have program ABCDE.

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Remember, in a program opposite sides are equal and parallel to that means is parallel to city and

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AC is parallel to Beatty.

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And remember, Abe is equal to KDDI in length and AC is equal to beauty in length.

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All right.

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Now let's join Vertex C and Vertex B, so you get two triangles, you have Triangle HCB and Triangle

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DBC So you have two triangles over here.

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Now let's observe some interesting things about these two triangles.

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You will see that angle.

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BCB is equal to angle C B, so this angle over here, DCB is equal to angle S.B.

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Now why is that so?

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Because these are alternate interior angles, right.

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You have a B parallel to Cirie and c.B is acting as the transversal.

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And we know in this case, alternate interior angles are equal.

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Similarly, you can see that Angle DBC is equal to Angle B.C. This angle over here is equal to this

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angle over here.

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Again, the reason is the same.

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AC is parallel to beauty and c.B is acting as a transposon.

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So alternating triangles are equal.

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That's why these two angles are equal.

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Now, KBE is equal to B.C. because it's a common sight.

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So this is a common sight.

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Now you can see when you observe these two triangles, you have two pairs of angles that are equal and

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the included side is equal.

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Therefore, Asper is a congruency.

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We can say that triangle ABC is congruent to triangle DCB, right?

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Remember, it has to be written in the correct way.

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You have A, B, C over here.

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Let's write ABC over here.

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Let's have a triangle over here.

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We know that angle ACB is equal to angle B, B, C, but over here is HCB.

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So angle D, B.C. also should be over here, right?

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That's why you have to over here.

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You have B over here and you have see or hear.

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These two angles are equal.

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So they are put in the same position and you have angle A, B, C is equal to angle the C, so that's

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also matching.

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These two are equal.

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Therefore Triangle ABC is congruently triangle DCB.

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Now this is Asper a congruency.

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Now let's move on.

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We have proof that these two triangles are congruent and hence we can see that angle C is equal to angle

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B, right.

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What is Anglesey angle sees nothing but angle B, C, B plus angle ECB.

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Right.

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We have the ECB over here and we have A, C, B over here.

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If I had these two together and if I had these two together, it would be the same.

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Right.

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So that's why we get here.

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That Angle C is equal to angle B.

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Similarly, you can prove that angle is equal to Angley.

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That's why the opposite angles of a program are equal.

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All right.

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Let's see one more property, which we saw before.

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We saw that the diagonals of a paragraph bisect each other.

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Right now, let's try to understand why that is so over here we have a program, ABCDE.

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Now, let me construct the two diagonals of this program.

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I have AC and BD and let them intersect at point.

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OK, all right.

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Now let's take a triangle or a B and OKd.

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OK, so this is all B and this is all C D right now, you will see that a B is equal to Katie.

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Why is that so?

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Because these are opposite sides of a battleground.

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And we know that in a battleground, opposite sides are equal.

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Anberlin so Abey's is equal to Kerry.

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Now we know that these two angles are equal right angles the or is equal to Angle or B.

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Why is that.

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So these are already interior angles, right.

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Because Abey's parallel to city and DBE is acting as a transversal.

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Therefore these two angles are alternating angles and we have angle B always equal to angle Krio.

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Similarly, we have angle DCO is equal to Angle or a C or a B.

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Why is that so.

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Because over here Abey's parallel to city and AC is acting as a transversal.

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So again these two are alternate interior angles.

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All right.

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Now therefore triangle aob is congruently, triangle C or D astbury as a rule now because these two

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triangles are congruent triangles, I can see that all is equal to or C and B is equal to Audy.

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Right.

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Or it will be equal to Ossy similarly.

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Or B as to be equal to Audy because these are corresponding parts of two congruent triangles.

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All right, so that's why we say that the diagonals in that program bisect each other that is always

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equal to U.S. and Audie is equal to or B.