Parallelogram

[vampirewitchreine]

This was a construction thing, but I don't have a compass..... could someone possibly tell me a program that would do the same thing that it's asking in the directions (Pictures from the book included).... Even though this seems like a simple problem, I'm only posting it due to lack of being able to follow the steps of the problem myself.

Construction: Parallelogram

Given two segments, construct a parallelogram with sides congruent to the segments.


1. Construct segment AB congruent to segment PQ


2. Construct segment BC congruent to segment RS


3. Draw an arc with center A and radius BC


4. Draw an arc with center C and radius AB. The arc should intersect the arc you drew in step 3.


5. Label the point where the arcs intersect D. Draw segment AD and segment CD/ ABCD is a parallelogram.





The following is the problem with which this is suppose to go with:

12. Writing Explain why ABCD must be a parallelogram.


(I also had the 2 following questions that go with this as well.... black is the question, blue is the type of question and the purple is my answer)

13. Open-ended Problem Describe two different ways to check that ABCD is a parallelogram. Show that both opposite sides are congruent and show that the diagonals intersect each other.


14. Writing How can you use the construction shown above to construct a rhombus? Lines RS and PQ would need to be congruent, making lines AB and BC congruent.




Sorry that the images are so poor.... my scanner is acting up and my webcam can't take a very clear picture.

 

[Deleted member 4993]

This was a construction thing, but I don't have a compass..... could someone possibly tell me a program that would do the same thing that it's asking in the directions (Pictures from the book included).... Even though this seems like a simple problem, I'm only posting it due to lack of being able to follow the steps of the problem myself.

Construction: Parallelogram

Given two segments, construct a parallelogram with sides congruent to the segments.
View attachment 1572

1. Construct segment AB congruent to segment PQ
View attachment 1573

2. Construct segment BC congruent to segment RS
View attachment 1574

3. Draw an arc with center A and radius BC
View attachment 1575

4. Draw an arc with center C and radius AB. The arc should intersect the arc you drew in step 3.
View attachment 1576

5. Label the point where the arcs intersect D. Draw segment AD and segment CD/ ABCD is a parallelogram.
View attachment 1577




The following is the problem with which this is suppose to go with:

12. Writing Explain why ABCD must be a parallelogram.


(I also had the 2 following questions that go with this as well.... black is the question, blue is the type of question and the purple is my answer)

13. Open-ended Problem Describe two different ways to check that ABCD is a parallelogram. Show that both opposite sides are congruent and show that the diagonals intersect each other.


14. Writing How can you use the construction shown above to construct a rhombus? Lines RS and PQ would need to be congruent, making lines AB and BC congruent.




Sorry that the images are so poor.... my scanner is acting up and my webcam can't take a very clear picture.

You need to buy a compass and protractor - those are fairly cheap and necessary implements if you continue with study-program where geometry & trigonometry are important.

 

[vampirewitchreine]

You need to buy a compass and protractor - those are fairly cheap and necessary implements if you continue with study-program where geometry & trigonometry are important.

I'd already had a protractor, and I went out this morning and got a compass.


I repeated this activity a few times to see what the result of a slight angle and a straight perpendicular set of lines would do (I also used lines of different sizes). When I have my lines at a slight angle I get a perfect parallelogram, nothing too specific about it. On the other hand, when I make the lines perpendicular to each other, I get a rectangle.

Should my answer to 12 be as followed?: The figure ABCD must be a parallelogram because opposite sides are both congruent and parallel.

Also should I change the first part of 13 to say: Prove that opposite angles are congruent? (Also rewording the second part to say prove that the diagonals are congruent instead of show?)

If you don't need the eraser, give it to Subhotosh:
he uses loads of them to erase his mistakes

I keep a bunch of erasers around because I make a ton of mistakes (Of course when I really need one, I can't find it)

 

[Deleted member 4993]

I'd already had a protractor, and I went out this morning and got a compass.


I repeated this activity a few times to see what the result of a slight angle and a straight perpendicular set of lines would do (I also used lines of different sizes). When I have my lines at a slight angle I get a perfect parallelogram, nothing too specific about it. On the other hand, when I make the lines perpendicular to each other, I get a rectangle.

Should my answer to 12 be as followed?: The figure ABCD must be a parallelogram because opposite sides are both congruent and parallel.

Also should I change the first part of 13 to say: Prove that opposite angles are congruent? (Also rewording the second part to say prove that the diagonals are congruent instead of show?)



I keep a bunch of erasers around because I make a ton of mistakes (Of course when I really need one, I can't find it)

Rectangles are special cases of parallelograms - and squares are special cases of rectangles (hence special case of parallelogram).

So your process led you to correct observation.

The definition of parallelogram is:

It is a quadrilateral polygon whose opposite sides are parallel.

Notice I did not specify the opposite sides are congruent. That is because if the opposite sides of a quadrilateral figure are parallel, in Euclidean space, those must be congruent.

 

[vampirewitchreine]

Rectangles are special cases of parallelograms - and squares are special cases of rectangles (hence special case of parallelogram).

So your process led you to correct observation.

The definition of parallelogram is:

It is a quadrilateral polygon whose opposite sides are parallel.

Notice I did not specify the opposite sides are congruent. That is because if the opposite sides of a quadrilateral figure are parallel, in Euclidean space, those must be congruent.

Okay, I changed my answer for 12 and took out the information about them being congruent (because- as you said- it's not a given that the opposite sides are, but it's a logical conclusion). But otherwise, are the rest of my answers okay?

 

[Mrspi]

Okay, I changed my answer for 12 and took out the information about them being congruent (because- as you said- it's not a given that the opposite sides are, but it's a logical conclusion). But otherwise, are the rest of my answers okay?

If you want us to evaluate your "final answers," PLEASE show us what you now have in your proposed "final form."

It's rather much to expect us to go through what you've previously posted, "add this and take out that" (whatever "this and that" might be) and determine what you mean. If you will do that, I will be happy to look them over and make constructive comments.

 

[vampirewitchreine]

If you want us to evaluate your "final answers," PLEASE show us what you now have in your proposed "final form."

It's rather much to expect us to go through what you've previously posted, "add this and take out that" (whatever "this and that" might be) and determine what you mean. If you will do that, I will be happy to look them over and make constructive comments.

Sorry about that.

Questions were:

12. Writing Explain why ABCD must be a parallelogram.

13. Open-ended Problem Describe two different ways to check that ABCD is a parallelogram.

14. Writing How can you use the construction shown above to construct a rhombus?


Okay, the final answers are as followed:

12. The figure ABCD must be a parallelogram because opposite sides are parallel.

13. To check if ABCD is a parallelogram, you must prove that the opposite angles are congruent and that the diagonals are congruent to each other (perhaps I should change this to prove that the opposite sides are congruent?)


14. In order to make ABCD rhombus, the lines PQ and RS would must be congruent, making AB congruent to BC congruent to CD congruent to AD.

 

[Mrspi]

Sorry about that.

Questions were:

12. Writing Explain why ABCD must be a parallelogram.

13. Open-ended Problem Describe two different ways to check that ABCD is a parallelogram.

14. Writing How can you use the construction shown above to construct a rhombus?


Okay, the final answers are as followed:

12. The figure ABCD must be a parallelogram because opposite sides are parallel.

13. To check if ABCD is a parallelogram, you must prove that the opposite angles are congruent and that the diagonals are congruent to each other (perhaps I should change this to prove that the opposite sides are congruent?)


14. In order to make ABCD rhombus, the lines PQ and RS would must be congruent, making AB congruent to BC congruent to CD congruent to AD.

The steps you took in the construction created a quadrilateral with both pairs of opposite sides congruent. You can draw a diagonal in such a quadrilateral, and prove the resulting two triangles are congruent, creating some equal alternate interior angles and two sets of parallel lines. I'm guessing that you have already DONE a proof that if both sets of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram. So, for #12, I think you need to say "I constructed a quadrilateral with both sets of opposite sides congruent. And if both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram (this should have been proved already).

For #13, in order to verify that this is a parallelogram, you can show that both pairs of opposite angles are congruent. BUT....the diagonals of a parallelogram are NOT generally congruent, so that would not be an appropriate way to show that this is a parallelogram. However, you should have showed that if the diagonals bisect each other, the quadrilateral is a parallelogram.

#14 is correct.

I do hope you realize that it is difficult to know for sure what your book has covered so far, because different texts may treat topics in a slightly different order. I'm basing my response here on what has most commonly appeared in the various geometry textbooks I've taught out of.

 

[vampirewitchreine]

The steps you took in the construction created a quadrilateral with both pairs of opposite sides congruent. You can draw a diagonal in such a quadrilateral, and prove the resulting two triangles are congruent, creating some equal alternate interior angles and two sets of parallel lines. I'm guessing that you have already DONE a proof that if both sets of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram. So, for #12, I think you need to say "I constructed a quadrilateral with both sets of opposite sides congruent. And if both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram (this should have been proved already).

For #13, in order to verify that this is a parallelogram, you can show that both pairs of opposite angles are congruent. BUT....the diagonals of a parallelogram are NOT generally congruent, so that would not be an appropriate way to show that this is a parallelogram. However, you should have showed that if the diagonals bisect each other, the quadrilateral is a parallelogram.

#14 is correct.

I do hope you realize that it is difficult to know for sure what your book has covered so far, because different texts may treat topics in a slightly different order. I'm basing my response here on what has most commonly appeared in the various geometry textbooks I've taught out of.

Thank you so much. Yes, I do understand that it can be difficult to do (I'm trying to make myself start posting what section I'm working on and any information that I can about what I'm using for my problem)

I actually started this course just before the school just before the school changed the textbook, so I'm actually working off of last year's course work versus the current because of the textbook switch (pages didn't correspond, so some of the pages that the new coursework was telling me to use, were pages of explanations instead of actually problems to work from). Even the school that I was at before enrolling in the current, my note order for what's in which chapter are in a different order [For example: My notes from my old school, chapters 2.1 and 2.2 are Conditional Statements. In my text, the same chapters are Types of Angles (2.1) and Classifying Triangles (2.2). Conditionals fall in chapters 3.5 and 3.7 in my book]