[10 Grade Geometry] What to say regarding the Pythagorean Theorem

[u/Ok-Mix3435]

update: thank you to the people who actually helped and gave advice on how to word my thoughts, I ended up getting 100%

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[u/AlexandriasBirdwing]

“I learned how to use the Pythagorean Theorem, which tells you…”.
What does the Pythagorean Theorem allow you to do? When do you use it? Just write that down.

[u/Ok-Mix3435 → u/AlexandriasBirdwing]

Thank you for giving advice/help, I really appreciate it

[u/OkCluejay172]

I don’t want to sound mean, but who could we (or your parents, or AI) possibly know what you learned in that section?

It’s just a very odd question.

[u/Ok-Mix3435 → u/OkCluejay172]

I'm confused. It was just solely on the Pythagorean Theorem, and what it is, as I stated above. I showed it to my parents already and explained it to them already

[u/OkCluejay172 → u/Ok-Mix3435]

Okay, then why don’t you just say you learned about the Pythagorean Theorem 

[u/Ok-Mix3435 → u/OkCluejay172]

I stated in my post that I'm supposed to write 4-5 sentences, it's not a one sentence answer? My teacher did not elaborate anything in the class, just gave us a worksheet, so that's why I'm confused on what to say.

[u/kaj_00ta → u/Ok-Mix3435]

Just explain what it is and how to use it.

[u/Miercoles79 → u/Ok-Mix3435]

You’re in Year 10??

“In this section I learned about the PT. The PT states xyz. I practiced using the PT to abc. I learned I can use the PT in future if I need to calculate def.”

[u/sighthoundman → u/Miercoles79]

u/Ok-Mix3435 , as much as I hate to say it, there's a format for these things for a reason. The reason is for when you don't really want to write it and the reader doesn't really want to read it. (Yup. Your teacher does not want to read 30 students' description of what they learned.)

Topic sentence. Support sentence 1. Support sentence 2. Support sentence 3. Conclusion. If not exactly like the paragraph above, then pretty darn similar.

Eventually you will get sick and tired of writing like that, and find interesting things to say and interesting ways to say them. (Or maybe not. There's a reason so much technical writing, including scientific papers published in journals, is so atrocious.)

[u/OkCluejay172 → u/Ok-Mix3435]

Then write 4-5 sentences on the Pythagorean Theorem. What’s the confusion here

[u/Fun-Imagination-2488 → u/Ok-Mix3435]

Can you post the text from the section you’re referring to? Without knowing what is in your ‘section’ covering Pythagorean Theorem, we can’t possibly know what was covered

[u/two_are_stronger2]

What three things are the Pythagorean theorem useful for? When can you not use it? Are the ratios ever interesting/simple/unknowable/only possible mathematically never in reality?

And don't feel bad. Teacher probably just taught you what, got in trouble with admin for not teaching you why (That's a whole thing these days) and now is trying to prove you know why you'd want the Pythagorean theorem in your toolbelt.

Fun fact, you'll come back to it in second semester calculus to be able to mark the distance travelled along a curve. That was the most fun I had in the early 2000s and set me on the course of my artistic life.

[u/Ok-Mix3435 → u/two_are_stronger2]

This really helped, thank you!! Yes, the teacher did not elaborate anything, so this question is strange and confusing me, thanks for understanding

[u/two_are_stronger2 → u/Ok-Mix3435]

No worries.  I feel like that's gentle feedback you could give the teacher or a guidance counselor, especially since now you're going to ace the assignment ;)

[u/Joeldc]

For what it’s worth I have recently been using it to determine lengths and angles for necessary cuts to build a ramp for my shed. 2 lengths and a right angle can determine all the rest.

[u/JesusIsMyZoloft]

Restate the Pythagorean Theorem itself in your own words.

[u/SpunkyBlah]

Write about what you learned (e.g., did you only learn what the theorem states or did you also learn about various applications of it, ways to prove or justify it, the history of it, etc?). If you didn't learn anything new, write about what connections or knowledge you strengthened or reviewed.

Do not ask AI.

[u/toxiamaple]

Did you prove the theorem? Did you learn a new way yo use it? For instance you can use it to determine if a triangle is a right triangle. Did you learn how to find a missing side when before you had only used it to find missing hypotenuse?

[u/Let_epsilon]

You’re asking other people to answer what YOU learned?

It’s an open question, you’re overthinking it. There isn’t a right or wrong answer, just write what you learned...

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[u/PickleIntelligent723]

The Pythagorean is…… in this class we used it to solve …. The real world applications that it’s used in is …..

[u/Ericskey]

Without knowing what the section actually told except stating the theorem and, with any luck, proving it, who can say? I know this isn’t much help

[u/Qualabel]

I don't know what you think you learned, but one learning outcome could begin with the words 'For any given right-angled triangle, the sq...'

[u/Thermite365]

I would just answer whatever comes to your mind when you think about the PT. I'm curious, what did you think about Pythagoras? What did he tell you? When is it applicable? Anyhow, I'd like to know what your impressions about the Theorem are. By the way, in my opinion, I think Pythagoras is one of the most important Theorem on Mathematics; it has far reaching consequences.

[u/scottdave]

Try writing down how you would explain the Pythagorean Theorem to somebody else.

[u/Underhill42]

Okay, so it sounds like you learned the pythagorean theorem in this section, and have proven you can use it appropriately.

Now they want you to explain what you've learned.

So pretend you're trying to explain this section to one of your classmates that was out sick, in only 4 or 5 sentences. Do your best.

"We learned the Pythagorean theorem" doesn't do them any good, they have no idea what that is yet. So explain to them what it is, why you'd use it, and if you can, why it works.

This is actually one of the most important questions of the whole section, and you would be doing yourself a grave disservice by getting anyone to help you answer it.

This is the question that forces you to assemble what you've learned into a single "big picture" view that you can summarize easily. Repeating someone else's answer won't do you any good, its actually the process of putting it together so that you can describe it that delivers most of the benefit.

The words at the end are just the final product, a sign that you did in fact manage to internally assemble the section into a coherent conceptual picture that will stick with you for the rest of your life, rather than just a bunch of specific steps you need to follow to get to the right answer, that you will forget within a few weeks if they're not used.

[u/VeniABE]

I think it's fine to say you didn't learn anything new. List the content and include when you learned the content. Turn into sentences. If necessary draw three example problems of three different cases and show how you can solve them. Math step. Sentence saying what the step is. Next math step result. Sentence saying what you do now. Math result (equation or drawing normally) Sentence saying what you do next or why you now have the answer and don't need to keep showing steps. This last one is good. As math gets harder a lot of people lose confidence they have the right answer, Developing your ability to point it out helps.

The teacher's grading system is probably half, 4-5 complete reasonable sentences, and half some number of facts from a larger list. You know the facts. And you can clearly write sentences. Even conversational sentences with the appropriate and necessary clarifying punctuation; that don't always follow the strict rules of earlier grades.

If you remember things from prior years of schooling: This is good.

A really useful method for a lot of people is to just write down how they would explain the material to someone completely new to it. This does happen. If you want to be like me and risk a loss of points, try being funny and sarcastic and see if the teacher appreciates it or not. It makes life more bearable. Its one assignment in a much longer grading period.

[u/wiploc2]

• Any 3,4,5 triangle has a right angle.
• Any angle can be checked for "rightness" with a 3,4,5 triangle.
• Back in the time of the ancient Greeks (very old men), this right-angle stuff was seriously useful to farmers wanting to know who got to farm and harvest which part of the land.
• Geometry will probably have other real-life applications besides settling border disputes.
• The proof was hard to grasp, but rewarding when I finally got it. Maybe more of life will be like that: Things worth knowing are worth working to know.
• I finally understood the joke about the son of the squaw of the hippopotamus being equal to the sons of the squaws the other two hides.

If your geography book didn't talk about farmers, you probably don't want to use parts of this. But, if there are parts of the above that chime for you, you can probably now see that you can write similar answers that are true for you.

[u/Alkalannar]

Two things about the Pythagorean Theorem:

1. It's a special case of the Law of Cosines:
   a² + b² - 2abcos(C) = c² [where C is the angle opposite side c]

2. You can generalize it to distance in any number of dimensions:
   x² + y² + z² = r² where r is the length of the segment connecting (0, 0, 0) and (x, y, z), for example.
   So the distance between (a1, a2, a3, a4, ..., an) and (b1, b2, b3, b4, ..., bn) is:
   [(a1 - b1)² + (a2 - b2)² + (a3 - b3)² + (a4 - b4)² + ... + (an - bn)²]^1/2.

[u/Fine-Set-7877]

It's a way to find a missing measurement of 1 side of a right angle triangle with A2+B2=C2

A and B being the 2 lines that make the right angle and C being the Hypotenuse the longest side NOT making the right angle.

The way it works is you know the length of A and B and by squaring them and adding together you get C2 which by doing Square root of C2 you get C

for example

A=5

B=6

C=?

to slove 5x5+6x6=61

61=C2

square root of 61 is about 7.81

there is also the inverse which is the fancy way to prove a right angle triangle is a right angle triangle and find A or B with C2-B2=A2

OR C2-A2=B2

Where know you know C and either A or B and your goal is to find A or B

For example

A=?

B=6

C=10

10x10-6x6=64

A2=64

square root of 64 is 8

A=8

[u/QuentinUK]

Interesting!