Pythagoras and His Theorem
You are either finished with your Pythagorean Theorem project or almost finished. Here are a few questions to ponder. You need to respond to one of these questions in a comment this week. Remember to use 6+1 writing traits.
1. Look at Q1 and Q2 in your handout. Have you specifically mentioned how each of the three vertices behaved? Explain in a comment.
2. What is a converse of a theorem (Refer to the last page of the handout). How are the activities different? Explain in a comment.
Today's Assignments:
1. Go to this website. Please do problems 1i, 1ii, 2, and 4 on a separate sheet of paper. All answers should be clearly written with explanations. Do not assume that numbers and symbols alone are sufficient. Use your 6+1 writing traits. This assignment is due on Thursday.
2. Begin preparing for your test on Thursday by reviewing your quizzes. You may need to come for help.
3. Read the In-Class Activity on page 52. You do not need the tiles; you can use graph paper like you did last week. You can answer the questions in your Math Journal. This should take no more than five minutes.
4. Lesson 1-9, Covering the Reading .
17 comments:
Hey Mrs. Burke!
I have a few questions about the Pythagorean Theorem. I'm not sure if I'm done or not. If I am done, should I print it out?
-AMS
Hi Mrs. Burke,
I started the questions on the web page and I'm having trouble with the 2nd one.
I'll just ask you tomorrow.
-wiesej
Are the Pythagoras' Theorem and the Pythagorean Theorem the same? I also had trouble with the second question in number 2. I am having trouble not using the theorem.
I forgot to leave the answer to one of the two questions that you asked. I looked at my handout and made sure that I did mention how the three vertices behaved. A and B are the points that behave the same for me. When I drag either one of them, the triangle rotates. C was the point that changed the shape of my triangle.
Hi Mrs. Burke,
For Q1 and Q2 two of the three vertices behaved the same. The legs of my right triangle were a and b, therefore leaving my hypotenuse to be c. Points A and B were the two vertices that behaved the same because they could both spin and change the size of right triangle. I'm assuming this has something to do with the fact that vertices A and B are the legs. Vertice C behaved differently in the sense that it only dragged the right triangle, though it didn't stay the same size.
I will answer problem 2 on the blog on a different comment since this one is already so long.
-AMS
Hi Mrs. Burke,
I meant to say that vertice C did not change the size of the triangle, vertice C only moved the shape, the same importance that the arrow has on our toolbar. And to answer the first question, yes, I had specifically mentioned the three vertices in my packet.
For the second problem, the converse theorem is if the sums of the squares on the two smaller sides of the triangle is equal to the sum of the square of the longest side of the triangle, then the triangle in the center is a right triangle.
The steps to follow in the Converse are different than the first steps we had to complete in this Pyhtagorean process because in the Converse they ask you to create an arbitrary or non-right triangle, to prove the Converse Theorem correct. The non-right triangle is like our control if this were a science experiment.
Sorry for writing so much!
-AMS
Hi Mrs. Burke,
thank you so much for clarifying the chapter to me!
For question 1 and 2 I think I did explain how each vertices act correctly. If the question means to explain what happens when you try to drag the vertices, then yes, I did answer it correctly. I wrote that if you move vertex (this is the singular of vertices, right?) C of the triangle, the shape of the triangle is changed, but the triangle is still a right triangle. Vertices A and B behaved the same. When I dragged either of them, the triangle just increases oro decreases in size, but the general shape stays the same.
I hope this is correct!
Also, I have another question about the test: Do we have to know what happens when we drag any vertex on our pythagorean theorem picture for the test?
-wiesej
Hi Mrs. Burke,
Thank you for your hint in math class for the website problems. I understand the pattern, I just don't know how to word it in a formula, could I make an example as my formula?
I also hope my answers to your blog questions were right, though now I'm not so sure.
-AMS
Hey Mrs. Burke,
I for the first question that we have to answer, do we have to answer Q1 and Q2, or do we just have to answer the wuestion after that. I ll be on later please reply.
Brendan
Hey Mrs. Burke,
I for the first question that we have to answer, do we have to answer Q1 and Q2, or do we just have to answer the wuestion after that. I ll be on later please reply.
Brendan
Hi Mrs. Burke,
In Q1 and Q2 I have mentioned what happens to each of the vertices a,d, and c. A and B act the same because when they are dragged the traingle rotates and changes in size. When you drag vertice c the traingle changes in size.
Brendan
Hi Mrs. Burke,
I did the question number two on the web page. First, it took me a while to find a pattern. But after a while, I got it! I enjoyed finding the answer, especially since I challenged myself to keep trying even if I didn't get it the first couple of tries and not ask anyone for help.
See you tomorrow!
-wiesej
Hey Mrs. Burke!
I finally got my measurements in my Pythagorean Teorem to correspond! Do we need to finish the Qs in the packet? For your blog questions, I checked my answers when I was working on my project, and I feel pretty confident with my answers. All I would like to add is what Carol said, that even though the size and placement of the triangle changes, the angles, or the triangle itself will never change.
See you tomorrow!
-AMS
Hi Mrs. Burke,
For Q1,when you try to move c, the angle stays 90 degrees and the triangle rotates. When you move a and b, the triangle changes size, but not shape.
Evan
Hi Mrs. Burke,
For Q1,when you try to move c, the angle stays 90 degrees and the triangle rotates. When you move a and b, the triangle changes size, but not shape.
Evan
for Q1 and Q2, A and B behave the same and C behaves differently. C changes the length of line BC thereby resizing the hypotenuse line, CA. A and B resize/rotate the triangle. I may be wrong though.
Is the Pythagorean Theorem a principle, and what is the difference between a theorem and a principle?
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