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Jilly
2/1/2023
Geometry
Flow Proofs
Flow proofs in geometry are a visual method for organizing logical steps in geometric proofs. They use arrows to connect statements and reasons, showing the progression of the proof.
2/1/2023
27
This page expands on the concept of flow proofs in geometry by presenting a more complex example involving linear pairs and angle relationships.
The example proves that angle JIK is a right angle given that L5 and L6 are a linear pair.
Definition: A linear pair consists of two adjacent angles that form a straight line, always summing to 180°.
The flow proof demonstrates several key geometric concepts:
Highlight: The given information in a flow proof can be presented in different locations within the proof, providing flexibility in organization.
Example: The proof uses the definition of a linear pair to establish that m∠5 + m∠6 = 180°, then progresses through several logical steps to conclude that ∠JIK is a right angle.
This example showcases how flow proofs in geometry can handle more complex relationships and multiple geometric concepts within a single proof structure.
Vocabulary: "Supplementary angles" are two angles whose measures sum to 180°, while "complementary angles" sum to 90°.
The page emphasizes the importance of clear reasoning and logical progression in constructing effective flow proofs for geometric arguments.
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Flow proofs in geometry are a visual method for organizing logical steps in geometric proofs. They use arrows to connect statements and reasons, showing the progression of the proof.
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This page expands on the concept of flow proofs in geometry by presenting a more complex example involving linear pairs and angle relationships.
The example proves that angle JIK is a right angle given that L5 and L6 are a linear pair.
Definition: A linear pair consists of two adjacent angles that form a straight line, always summing to 180°.
The flow proof demonstrates several key geometric concepts:
Highlight: The given information in a flow proof can be presented in different locations within the proof, providing flexibility in organization.
Example: The proof uses the definition of a linear pair to establish that m∠5 + m∠6 = 180°, then progresses through several logical steps to conclude that ∠JIK is a right angle.
This example showcases how flow proofs in geometry can handle more complex relationships and multiple geometric concepts within a single proof structure.
Vocabulary: "Supplementary angles" are two angles whose measures sum to 180°, while "complementary angles" sum to 90°.
The page emphasizes the importance of clear reasoning and logical progression in constructing effective flow proofs for geometric arguments.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the concept of flow proofs in geometry, providing a visual alternative to traditional two-column proofs. Flow proofs use arrows to connect statements, illustrating the logical progression of a geometric argument.
Definition: A flow proof in geometry is a method of organizing statements connected by arrows to show the flow of logical reasoning, with reasons provided underneath each statement.
The page presents an example of a flow proof, demonstrating how to prove that y = 55 given that x + y = 60 and x = 5.
Example: In the flow proof example, the given information is used as a starting point. The proof then progresses through substitution and subtraction to reach the conclusion that y = 55.
Highlight: The layout of a flow proof can be flexible. As long as the statements are in the correct logical order, the shape of the flow can vary.
The page also touches on the concept of equality in geometric proofs, using an example involving m² = 90.
Vocabulary: "Given" refers to the initial information provided in a geometric proof, which serves as the starting point for logical reasoning.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
