How can I change the angles of parallelogram to become trapezoid?

shahar

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How can I change the angles of parallelogram to become trapezoid?
 
How can I change the angles of parallelogram to become trapezoid?
What have you tried? Where are you stuck? What is preventing a parallelogram from being a trapezoid?

Please show us some work so we know what you need help with.
 
It is an experment

I have a quadriletal that is a parralogram with angle alpha, beta, gamma and delta.
I have a trapozoid with angle alpha2, beta2, etc.
sin(alpha) = cos(alpha2)
What is values alpha can be?
 
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Answer

What have you tried? Where are you stuck? What is preventing a parallelogram from being a trapezoid?

Please show us some work so we know what you need help with.
What is preventing a parallelogram from being a trapezoid?
The trapoezoid have two pair of non-parallel sides that are parallel in the parallelogram !!!
 
What is preventing a parallelogram from being a trapezoid?
The trapoezoid have two pair of non-parallel sides that are parallel in the parallelogram !!!
That is not true!!! A trapezoid is a four sided figure that does have one pair of opposite sides parallel. In fact, the definition does NOT say that both pairs of opposite sides can't be parallel. Hence all parallelogram are trapezoids.
 
I have a quadriletal that is a parralogram with angle alpha, beta, gamma and delta.
I have a trapozoid with angle alpha2, beta2, etc.
sin(alpha) = cos(alpha2)
What is values alpha can be?
A quadrilateral has only two distinct angles, so no need to have alpha, beta, gamma and delta. In fact just knowing alpha is enough to know the four angles (given alpha, beta = 180 - alpha).
 
I have a quadriletal that is a parralogram with angle alpha, beta, gamma and delta.
I have a trapozoid with angle alpha2, beta2, etc.
sin(alpha) = cos(alpha2)
What is values alpha can be?

I think we need more information. Could you show us a picture of what you are doing?

When you say "I have ...", do you mean both are given? Or, as your title implies, are you given the parallelogram and want to make a trapezoid with the indicated relationship? Or, as your question here suggests, is it the trapezoid that is known?

Can you see how the angles alpha and alpha2 will be related? Once you have found alpha2, one other angle will be known, but the rest of the trapezoid is free -- you can't determine all sides and angles from only what you have told us. So there must be more to the problem.

It is very important that you tell helpers the entire problem.
 
A quadrilateral having two and only two sides parallel is called a trapezoid.

However, most mathematicians would probably define the concept with the A quadrilateral having at least two sides parallel is called a trapezoid.

Whichever definition you choose from above, a trapezoid does have a pair of parallel sides. You said that a trapezoid has no parallel sides.

In my opinion when you want the definition of a mathematical term you should use the one that mathematicians use.

 
I think we need more information. Could you show us a picture of what you are doing?

When you say "I have ...", do you mean both are given? Or, as your title implies, are you given the parallelogram and want to make a trapezoid with the indicated relationship? Or, as your question here suggests, is it the trapezoid that is known?

Can you see how the angles alpha and alpha2 will be related? Once you have found alpha2, one other angle will be known, but the rest of the trapezoid is free -- you can't determine all sides and angles from only what you have told us. So there must be more to the problem.

It is very important that you tell helpers the entire problem.
I have = given. Or both (the paralleogram and trapezoid) are given.
(1) I don't understand. Why I need two angle that are given?
(2) Can the other angle be calculate by 180-anglevalue?
(3) What the diffuclity with what I ask? - I read your reply and I don't understand.
 
I have = given. Or both (the paralleogram and trapezoid) are given.
(1) I don't understand. Why I need two angle that are given?
(2) Can the other angle be calculate by 180-anglevalue?
(3) What the diffuclity with what I ask? - I read your reply and I don't understand.

I think you are saying the problem is something like this:

Two quadrilaterals are given: one is a parallelogram with angles alpha, beta, gamma, and delta; the other is a trapezoid with corresponding angles alpha2, beta2, gamma2, and delta2.
If we know that sin(alpha) = cos(alpha2), what are the possible values of alpha?

One trouble is that if both quadrilaterals are given (that is, either you are told all the necessary facts about each of them, or you are just told that they exist, with some fixed dimensions you don't know), then both alpha and alpha2 are equally fixed - you aren't changing one into the other, or creating one given the other.

If the value of alpha is known, then the question is meaningless (it has the given value!); if not, then it has to be assumed (though it wasn't stated) that alpha2 is known, and alpha has to be determined in terms of alpha2. So the question has to mean, "If sin(alpha) = cos(alpha2), what value can alpha have, in terms of alpha2?" Without knowing alpha2, we can't figure out what alpha is.

You've answered that sort of question (finding one angle given the other), though not quite correctly: If the sines the two angles were equal, then the angles would be either equal or supplementary. What can we infer about their relationship if the sine of one equals the cosine of the other?

But also notice that the question deals only with one angle in each figure, so all that has been said about parallelograms and trapezoids is irrelevant! There is no reason to have the first sentence. This is why I said there must be more to the problem: There is too much information to answer the question, and there is too little information to say anything about the rest of the figures.

So, what is this "experiment" that evidently motivates the question? And in what sense are you asking about "changing" angles in one figure to make it another?
 
thinking on the question

Can one give me in list of detail why it is impossible to answer the question?
The solution can be written in computer language.
 
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Can one give me in list of detail why it is impossible to answer the question?
The solution can be written in computer language.

Who said it was impossible to answer the question? That is very simple, if we take it as stated; as I said, you came close.

alpha = ___ - alpha2 or alpha = ___ + alpha2.

What goes in each blank?

My concern is that the question is not related to what is said about the two figures (and those figures are central to the problem, according to the title you gave it), so you clearly have not stated the real problem. Now that you mention "computer language" (which one?), that is even more certain, since that has not been part of the problem until now.

As we ask in https://www.freemathhelp.com/forum/threads/41537-Read-Before-Posting!!, please "Post the complete text of the exercise".
 
answer

The instruction of writting in computer language was not mention in the page of the question but in the end of the text of the work.
But the near the title was written read all the text before answering. (My mistake that I don't follow it :)())
I don't know what is in the blank.
I know only that there is supplement angles as you said. But, I guess maybe 180. But I don't know (!!).
 
The instruction of writting in computer language was not mention in the page of the question but in the end of the text of the work.
But the near the title was written read all the text before answering. (My mistake that I don't follow it :)())
I don't know what is in the blank.
I know only that there is supplement angles as you said. But, I guess maybe 180. But I don't know (!!).

Can you please show us what you are seeing, so we can help you better??? You have now admitted that there is more that we haven't seen. We need a clue. Quote the entire problem, or attach a picture of the page (being careful to check that it is clear after attaching it).

But let's focus on the question: If we know that sin(A) = cos(B), what are the possible values of A in terms of B? Start with a simpler question: how are these angles related? There is an identity you should know that relates the sine and cosine (it may be called a "co-function" identity). Find a list of identities, or look at the definitions of the trig functions, and you should find it.
 
A quadrilateral has only two distinct angles, so no need to have alpha, beta, gamma and delta.
In fact just knowing alpha is enough to know the four angles (given alpha, beta = 180 - alpha).

I don't know how you are making this claim.

Picture convex Quadrilateral ABCD on the xy-axes. Let point C be at the origin and let angle C have a measure of 75 degrees.
Let point D be to the right of point C and also on the x-axis, and let angle D have a measure of 60 degrees. Let side CD be
the longest side of the quadrilateral. (Extend it as needed.)

Let points A and B be in Quadrant I. Let the measure of angle B be 90 degrees and the measure of angle A be 135 degrees.
The sum of the four interior angles is 360 degrees (necessarily for a quadrilateral).

Imagine building the quadrilateral up from the x-axis from scratch. You have the side CD. The sizes of angles C and D are
independent of each other. Side BC is a side of the angle C, and side AD is a side of the angle D. Those two side lengths are not
set. Therefore, the measures of angles A and B can vary.

What I see supported in this context is: "If you know the measures of three unique interior angles of a general quadrilateral,
then the measure of the fourth interior angle is determined. ** However, if you know the measures of exactly two unique interior
angles of a general quadrilateral, then the measures of the two remaining interior angles will not necessarily be able to be
determined."



** . . . For example, m<B = 360 degrees - (m<C + m<D + m<A)
 
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How can I change the angles of parallelogram to become trapezoid?

A quadrilateral has only two distinct angles, so no need to have alpha, beta, gamma and delta. In fact just knowing alpha is enough to know the four angles (given alpha, beta = 180 - alpha).

I don't know how you are making this claim.

Picture convex Quadrilateral ABCD on the xy-axes. Let point C be at the origin and let angle C have a measure of 75 degrees.
Let point D be to the right of point C and also on the x-axis, and let angle D have a measure of 60 degrees. Let side CD be
the longest side of the quadrilateral. (Extend it as needed.)

I think Jomo meant to say that a parallelogram has only two distinct angles, which are supplementary. What he said makes sense that way.
 
It is an experment … I have a quadriletal that is a parralogram with angle alpha …

I have a trapozoid with angle alpha2 …

sin(alpha) = cos(alpha2)

What is values alpha can be?
Here's another interpretation, using complimentary angles.

α + α2 = 90°

This satisfies:

sin(α) = cos(α2)

paratrap.jpg

For example (angles rounded):

α = 64.3°

α2 = 90° - 64.3° = 25.7°

sin(64.3°) = cos(25.7°)

I don't know your experiment, but you could program a computer to draw the trapezoid above, given alpha and the parallelogram's upper base and side lengths (to match the trapezoid's sides, respectively).

Note: I didn't draw the trapezoid's upper base long enough to match the parallelogram's, and I'm too lazy to edit the diagram. 8-)
 
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I don't know how you are making this claim.

Picture convex Quadrilateral ABCD on the xy-axes. Let point C be at the origin and let angle C have a measure of 75 degrees.
Let point D be to the right of point C and also on the x-axis, and let angle D have a measure of 60 degrees. Let side CD be
the longest side of the quadrilateral. (Extend it as needed.)

Let points A and B be in Quadrant I. Let the measure of angle B be 90 degrees and the measure of angle A be 135 degrees.
The sum of the four interior angles is 360 degrees (necessarily for a quadrilateral).

Imagine building the quadrilateral up from the x-axis from scratch. You have the side CD. The sizes of angles C and D are
independent of each other. Side BC is a side of the angle C, and side AD is a side of the angle D. Those two side lengths are not
set. Therefore, the measures of angles A and B can vary.

What I see supported in this context is: "If you know the measures of three unique interior angles of a general quadrilateral,
then the measure of the fourth interior angle is determined. ** However, if you know the measures of exactly two unique interior
angles of a general quadrilateral, then the measures of the two remaining interior angles will not necessarily be able to be
determined."



** . . . For example, m<B = 360 degrees - (m<C + m<D + m<A)
I meant parallelogram, not quadrilateral
 
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