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In parallelogram abcd what is dc?
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The parallelogram ABCD shows the points P and Q dividing… – Quora – ABCD is a parallelogram, E is the midpoint of BC and F is the midpoint of BE. What is the ratio to the area of a triangle AFC to the area of the Can you solve this equation in under 20 seconds? If so, you are likely to be in the top 5% of players in this award-winning strategic city building game.The diagonals of a parallelogram are not always equal in length. If you draw a line from point B to line AD, you'll see that line BD travels a horizontal To find the length of CD use Pythagorean Thm… CD= sqrt(4^2+2^2) = 2sqrt(5) CD = AB AD + DC + CB + BA = 12 + 2sqrt(5) + 12 + 2sqrt(5) = 24 + 4sqrt(5).Different Taxes in India. Practical VAT CST. Practical Service Tax. Ex 9.2, 1 – Chapter 9 Class 9 Areas of Parallelograms and Triangles. Last updated at June 29, 2018 by Teachoo.
Ex 9.2, 1 – In figure, ABCD is parallelogram, AE DC and CF AD. If AB – Parallelogram is a quadrilateral whose opposite sides are parallel and pairwise equal(lie on parallel lines).. Parallelograms differ in size of an adjacent sides and angles but Quadrilateral ABCD is a parallelogram, if at least one of the following conditions: 1. Quadrilateral has two pairs of parallel sidesSince ABCD is a parallelogram, line AB and line DC are parallel and has the same value.To solve this, equate line AB to be equal with line DC.So,Line AB = Line DC(9x-14)in = (3x +4)inNext group like terms to get the value of x9x in-3x in = 4in+14in = x =. 3inSince, we now have the value of xClick here to get an answer to your question In parallelogram ABCD, what is DC? This is a parallelogram which means the two opposites sides are equal. Then, we can solve the problem as shown below: mAB = m DC 9x -14 = 3x + 4 Transpose and combine same term: 9x – 3x =4 +14 6x…
Parallelogram: Supplementary Angles – Look at the picture on the screen.
we have a boy Raghav, who has been given a very tedious task. He has been asked to find
out the angles of the field of a school, the field ABCD. Now it was told to him that this
field is in the shape of a parallelogram that is opposite sides are parallel to one another.
Now Raghav had been asked out to find out the angles, angle A, angle B, angle C and
angle D of this particular field, but the problem was that this field was a huge one
and Raghav was a lazy boy. So, he did not want to go around the field measuring all
the four angles so, what he did do. Raghav was a boy who knew his mathematics very well.
So, what he did was he measured just one of the angles and after measuring only one angle,
he was able to find out the measures of all the other 3 angles correctly. So, let us see
how Raghav did this and what property of a parallelograms he used. So, the property is
that consecutive angles of a parallelogram are supplementary. So, what do I mean when
I say supplementary, it means that the sum of the angles is equal to 180°. So, in this
case when I say consecutive angles, I mean either angle A and angle B or angle B and
angle C and likewise, angle C angle D and in a similar manner. So, in this case we have
considered two angels. In this parallelogram we have considered angle X and angle Y and the
property states that consecutive angles in this case angle X and Y will be supplementary.
So, we write X plus Y is equal to 180°. So, in a simple way we can prove this with a very
simple activity. Over here I take this particular portion that resembles the triangle. I take
this portion and I move it to this side. Since opposite sides are parallel to one another,
I was able to do this very simply. Now, as you can see angle X and angle Y lie on a straight
line or in other words they form a linear pair of angles. So, since angle X and angle
Y are a linear pair of angles or in other words they lie on a straight line we can say
easily, that X plus Y is equal to 180°. Now, let us find out how we can prove this property
mathematically. So, we have been given ABCD, which is a parallelogram and we have been
asked to prove that angle ABC that is this angle is equal to angle DAB that is this angle.
So what have we been given? We have been given that ABCD is a parallelogram, that is this
side and this side are parallel and these two sides are also parallel to one another.
Thus AD parallel to BC and AB parallel to DC have been given to us. So, now let us see
how we can proceed to prove this particular property. Now, in the beginning what we do
is, we consider parallel sides AD and BC. So, we consider these two sides and we extend
line AB to E. Now if you look closely, you will find that AD is parallel to BC. So I
mark out two angles now, angle DAB and angle CBE. If you look closely you will find that
angle DAB and angle CBE are corresponding angles for the parallel sides AD and BC and
from the property of parallel lines we know, that corresponding angles are equal. So, I
can write that angle DAB is equal to angle CBE, because they are corresponding angles.
Now, we have established these two angles are equal, by virtue of the fact that they
are corresponding angles. Now consider another angle that is angle CBA, now in angle CBA
or angle ABC and angle CBE, we find that these two angles are lying on a straight line or
in other words we can say that angle ABC plus angle CBE is equal to 180°, why? Because
these two angles lie on the straight line AE and they form a linear pair of angles,
thus angle ABC plus angle CBE equal to 180°, because they form linear pair. Now look at
this particular equation, which we had obtained earlier and used this value in this equation.
So, I can replace the value of CB with angle DAB and what do I obtain, I obtained angle
ABC plus angle DAB is equal to 180°. I merely replace the value obtained from this equation
into this equation and I obtained angle ABC plus angle DAB is equal to 180°. This is
nothing but what we had originally set out to prove, that angle ABC plus angle DAB that
are consecutive angles for the parallelogram ABCD, the sum of these two angles is equal
to 180°, thus we have proved this particular property. So, consecutive angles of a parallelogram
are supplementary. So, now Raghav was able to measure as I mentioned previously, one
angle of the entire huge parallelogram field and that angle is equal 50° and measuring
only this particular angle, Raghav was able to find out all the other three angles, so
let us see how. So we have studied that, consecutive angles in a parallelogram are supplementary,
so if I have the measure of this particular angle, angle DAB and I have been given that
ABCD is a parallelogram, what can I say. I can say that angle DAB plus angle ABC will
be equal to 180° and we know the value of angle DAB that is DAB is equal to 50°, so
I can write 50 plus angle ABC is equal to 180°. So, now from this equation I can easily
calculate the value of angle ABC, that is this particular angle, How? I simply take
fifty to the other side, that is 180 minus 50 is going to give the measure of angle ABC,
and that gives me 130°, so I get the measure of angle ABC as 130°. So, in a similar manner
we can find out the measures of all the other angles, if we consider two other consecutive
angles, let's say angle DAB and angle CDA that is this angle which is equal to 50°
and this angle, even in this case these two angles are consecutive and these two angles
will be supplementary. So, also over here angle CDA will be equal to 180° minus 50°
which is equal to 130°. So, CDA or ADC is equal to 130° and again in a similar manner
considering angle ABC is a consecutive angle with angle BCD, that is this particular angle
and they will be supplementary as well, we can easily find out the measure of that angle.
So, angle DCB that is this particular angle will also be equal to 50°, why? Because,
angle ABC and angle DCB are consecutive angles. So, it was in this way knowing just one value
of one angle, that is angle DAB Raghav was able to measure all the other 3 angles using
this particular property .
Geometry 7.3d – Opposite Sides Parallel and Equal – .
Parallelogram: Bisectors of Consecutive angles – We have studied about various properties of parallelograms, rectangles as well as rhombuses and we have also seen that rectangles and rhombus are special cases of a parallelogram.
Now we are going to discuss about certain advanced properties of these and in greater detail. So the first property that we discuss is that of a parallelogram. It states that in a parallelogram, the bisectors of any two consecutive angles intersect each other at 90 degrees. So if I consider the bisector of A and bisector of B, these angular bisectors will intersect at 90 degrees. Similarly if I consider angle A and angle D, their angular bisectors would also intersect at 90 degrees. So for the proof we have considered the angular bisectors of A and B and we have to prove that they actually intersect at 90 degrees that is angle AOB is equal to 90 degrees. So this is what we have to prove and what have we been given? We have been given that ABCD is a parallelogram or in other words AB is parallel to DC and AD is parallel to BC. So this is what we have been given. Now with this information, let us see how we can proceed. So firstly we consider the entire angle A and the entire angle B. Now since ABCD is a parallelogram we have seen that consecutive angles in a parallelogram are supplementary or in other words angle A plus angle B will be equal to 180 degrees. Thus angle A plus angle B is equal to 180 degrees because consecutive angles of a parallelogram are supplementary. Now in this equation I divide by two or I multiply by half on both sides. So I write half angle A plus half angle B is equal to half of 180 degrees. So it is nothing but half A plus half B equals 90 degrees because 180 by 2 is 90. thus I get half of A plus half of B is equal to 90 degrees. Now look closely over here. If I'm considering half of A and half of B, I can say that angle one is half of A and angle two is half of B. So further I can write that angle 1 plus angle 2 is equal to 90 degrees. So angle 1 plus angle 2 equals 90 degrees, why, because we have been given that AO is the angular bisector of angle A and BO is the angular bisector of angle B. Thus half of A means angle one and half of B means angle two. Angle 1 plus angle 2 is equal to 90 degrees. Now consider the triangle AOB. In triangle AOB, the sum of angle 1 and 2 is equal to 90 degrees, so how can I write angle AOB? You know that in a triangle the sum of the interior angles is 180 degrees. So I can write angle AOB plus I can write angle AOB plus one plus angle 2 is equal to 180 degrees. Thus, in triangle AOB, this is what I can write angle AOB plus angle 1 plus angle 2 equals 180 degrees. Now angle 1 plus angle 2 is equal to 90 degrees as we have previously obtained, so this is 90 degrees. So how can I right angle AOB? Angle AOB in that case will be equal to 180 and I take angle one plus angle two to the other side that is angle 1 plus angle two. So angle one less angle 2 is equal to 90 degrees. So what will I get angle AOB as. Angle AOB will be 180 degrees minus 90 degrees. Thus this gives me angle AOB that is AOB as 90 degrees. So be get what we had originally set out to prove that is the angular bisectors of angle A and angle B intersect each other at right angles or in other words, angle AOB is equal to 90 degrees and we have proved this mathematically. Now this proof can be extended to prove another property. This property states that the angle bisectors of a parallelogram form a rectangle or in other words over here we are considering the angular bisectors of all the four angles. Angle A angle B angle C and angle D, all these are angular bisectors. Now it has been given to us that PQRS is a figure being formed and we have to prove that it is a rectangle. So previously we saw that when we are considering angle A and angle B, their angular bisectors intersected each other at 90 degrees. Now similarly we consider any other two angular bisectors, consecutive angles B&C for example. They are intersecting at a point and from the previous proof we know that if we consider angular bisectors of two consecutive angles, they will intersect act 90 degrees. Now if you look closely you will find that this angle and this angle are vertically opposite and what is the property of vertically opposite angles that they are equal. So if this is equal to 90 degrees this will also be equal to 90 degrees. In a similar manner if I consider the angular bisectors of D and C, they will also intersect at 90 degrees. Likewise, angular bisectors of D and A will also intersect at 90 degrees and since these two angles are vertically opposite, this angle will also be 90 degrees. So thus we see that in the quadrilateral PQRS, all four internal angles are equal to 90 degrees and thus PQRS is a rectangle and thus it proves the property that angle bisectors of a parallelogram form a rectangle. .