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Students in this video, let's discuss about Parallelograms Parallelograms are a special kind of quadrilaterals,

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that is, they are also foresighted polygons, but in a program you will see that the opposite sides

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are equal.

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Anberlin.

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All right.

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Now let's discuss five interesting properties about Parallelograms.

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And later in this course, we will prove some of them so that you can understand why these properties

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are so and that will help you retain whatever we learn.

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All right.

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Let's start with properties of a Barlowe Graham ASPO Constriction and definition.

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The opposite sides of a program are equal and parallel.

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But what does that mean?

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It means that a B is equal to code in length and AC is equal to BD in length and B is parallel to city

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and AC is parallel to Beatty.

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So only if this is true, we call the shape as a program.

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All right, now let's move on.

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The next interesting property about the program is that opposite angles of a program are equal.

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Now, that means Angley is equal to Angle D. And Angle C is equal to angle B.

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Now you can prove this using congruent triangles, like if you join c.B, you will get two concurrent

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triangles.

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Now we will see that in a future video.

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All right, let's press on the next interesting property of programs.

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Is that diagonals beside each other?

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So let's draw the diagonals of this program, ABCDE over here.

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So that would be Hédi and c.B and let the point of intersection of these two diagonals be.

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All right.

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Ask for this property.

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We can see that equal is equal to Audy and C O is equal to Olby.

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Now this also can be proved with the help of congruent triangles.

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If you take any two triangles, for example, if you dig it will be and see already you can see that

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these two are congruent and that's why it is equal to three and all is equal to or B, we will see that

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in a future video.

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All right, let's press on.

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You can also see that in the case of a from the some of the adjacent angles is equal to 180 degrees.

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So let's take an example.

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Angle A plus angle B would be 180 degrees or the are supplementary.

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That is this angle plus this angle will give you 180 degrees.

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Similarly, this angle plus this angle, that is angle A plus Anglesey also gives you 180 degree.

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And remember, this is derived from the property that the consecutive interior angles of.

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Two parallel lines cut by a transversal or supplementary right over here, Abey's parallel to City and

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AQ's acting as the transversal, so angry and Anglesey are consecutive interior angles on the same side

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of the transposon.

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Right and that's right.

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Angle E-Plus angle is equal to 180 degrees.

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Similarly X parallel to beauty and abs acting as the transposon.

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That's right.

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Angle E-Plus, angle B is equal to 180 degrees.

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All right.

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So we have seen so far four interesting properties.

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Let's get to the next interesting property if you take any collateral.

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But this is inequal is not necessarily a program.

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If you take any collateral and you identify the midpoints of its sides and if you join these together,

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you will get a program.

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If you take any collateral and you join the midpoints, you get a parallelogram.

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So we have seen five interesting properties of a program.

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Opposite sides are equal and parallel opposite, and these are equal diagonals beside each other and

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some of the edges and angles is equal to 180 degrees.

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All right.

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Now we will prove these in future videos and these properties will help us solve a lot of questions.