Students in this video, let's discuss about Parallelograms Parallelograms are a special kind of quadrilaterals,
that is, they are also foresighted polygons, but in a program you will see that the opposite sides
are equal.
Anberlin.
All right.
Now let's discuss five interesting properties about Parallelograms.
And later in this course, we will prove some of them so that you can understand why these properties
are so and that will help you retain whatever we learn.
All right.
Let's start with properties of a Barlowe Graham ASPO Constriction and definition.
The opposite sides of a program are equal and parallel.
But what does that mean?
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
and AC is parallel to Beatty.
So only if this is true, we call the shape as a program.
All right, now let's move on.
The next interesting property about the program is that opposite angles of a program are equal.
Now, that means Angley is equal to Angle D. And Angle C is equal to angle B.
Now you can prove this using congruent triangles, like if you join c.B, you will get two concurrent
triangles.
Now we will see that in a future video.
All right, let's press on the next interesting property of programs.
Is that diagonals beside each other?
So let's draw the diagonals of this program, ABCDE over here.
So that would be Hédi and c.B and let the point of intersection of these two diagonals be.
All right.
Ask for this property.
We can see that equal is equal to Audy and C O is equal to Olby.
Now this also can be proved with the help of congruent triangles.
If you take any two triangles, for example, if you dig it will be and see already you can see that
these two are congruent and that's why it is equal to three and all is equal to or B, we will see that
in a future video.
All right, let's press on.
You can also see that in the case of a from the some of the adjacent angles is equal to 180 degrees.
So let's take an example.
Angle A plus angle B would be 180 degrees or the are supplementary.
That is this angle plus this angle will give you 180 degrees.
Similarly, this angle plus this angle, that is angle A plus Anglesey also gives you 180 degree.
And remember, this is derived from the property that the consecutive interior angles of.
Two parallel lines cut by a transversal or supplementary right over here, Abey's parallel to City and
AQ's acting as the transversal, so angry and Anglesey are consecutive interior angles on the same side
of the transposon.
Right and that's right.
Angle E-Plus angle is equal to 180 degrees.
Similarly X parallel to beauty and abs acting as the transposon.
That's right.
Angle E-Plus, angle B is equal to 180 degrees.
All right.
So we have seen so far four interesting properties.
Let's get to the next interesting property if you take any collateral.
But this is inequal is not necessarily a program.
If you take any collateral and you identify the midpoints of its sides and if you join these together,
you will get a program.
If you take any collateral and you join the midpoints, you get a parallelogram.
So we have seen five interesting properties of a program.
Opposite sides are equal and parallel opposite, and these are equal diagonals beside each other and
some of the edges and angles is equal to 180 degrees.
All right.
Now we will prove these in future videos and these properties will help us solve a lot of questions.