Let's do this question, ABCDs, a rhombus such that the perpendicular by sector of a B passes through
the find the angles of the rhombus.
All right, pause the video, give it a try, and then let's do it together.
All right.
We're back.
Let's do it together.
Now, let the side of the rhombus be X units.
All right.
So, A.B., is it easy to see the glue?
Because it looks all right now.
Let's join B, Andy.
So that's one of the diagonals, right?
All right.
Now let's analyze triangles deep, deep and triangle DBP.
So these two triangles.
All right, we will find that these two triangles are congruent.
Now, why is that?
So you have beauty is equal to peaty.
That's a common sight.
Right.
And you have angle apre is equal to angle.
Beauty is equal to 90 degrees.
Right.
Because it's mentioned that the perpendicular by sector of Ebbe.
Oh, that's a 90 degree over here d this is given.
All right.
And you have EHP is equal to PB because it's a perpendicular bisecting.
So that's why therefore these two triangles are congruent.
Asper artists congruency ruled now because these two are congruent.
I can say it is equal to beauty because they are corresponding sides of these two corresponding congruent
triangles.
All right.
Now, because it is equal to beauty, I can say that a b.
Beat that this triangle over here is an equal triangle, right, because it is X, Sabeti also will
be X, all the sides are of equal length to triangle.
EBD is an equilateral triangle.
All right.
Therefore, angle is equal to 60 degrees.
Now we can easily find all the remaining angles, right?
We can see that angle B is 120 degrees.
Angle C, 60 degree angle D is 120 degrees because a rhombus is a parallelogram.
Right.
To do so because of this.
What happens, we know that opposite angles in a program are equal to angle a 60.
So we get Anglesey is also equal to 60.
And we know that in a bar looking at different angles are supplementary.
But this is 60.
So this angle over here will be 180 minus 60.
That's 120 degree.
And this angle and this angle are equal.
So this is also equal to 120 degrees.