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Fun with Flow Proofs in Geometry: Examples, Worksheets, and PDFs

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Fun with Flow Proofs in Geometry: Examples, Worksheets, and PDFs

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.

  • Flow proofs offer a flexible alternative to two-column proofs
  • They emphasize the logical flow of reasoning in geometric arguments
  • Key components include given information, statements, reasons, and a conclusion
  • Flow proofs can be adapted to various geometric problems and theorems

2/1/2023

27

(29)
Flow Proof
Flow Proof: statements connected by arrows
to show the flow (reasons are underneath
each statement)
x + y = 60
x=5
given
Exa

Introduction to Flow Proofs in Geometry

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 (x + y = 60 and x = 5) 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.

(29)
Flow Proof
Flow Proof: statements connected by arrows
to show the flow (reasons are underneath
each statement)
x + y = 60
x=5
given
Exa

View

Applying Flow Proofs to Complex Geometric Problems

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:

  1. Properties of linear pairs
  2. Right angle definition
  3. Supplementary angles
  4. Congruent angles
  5. Perpendicular lines

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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Fun with Flow Proofs in Geometry: Examples, Worksheets, and PDFs

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.

  • Flow proofs offer a flexible alternative to two-column proofs
  • They emphasize the logical flow of reasoning in geometric arguments
  • Key components include given information, statements, reasons, and a conclusion
  • Flow proofs can be adapted to various geometric problems and theorems

2/1/2023

27

 

Geometry

1

(29)
Flow Proof
Flow Proof: statements connected by arrows
to show the flow (reasons are underneath
each statement)
x + y = 60
x=5
given
Exa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to Flow Proofs in Geometry

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 (x + y = 60 and x = 5) 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.

(29)
Flow Proof
Flow Proof: statements connected by arrows
to show the flow (reasons are underneath
each statement)
x + y = 60
x=5
given
Exa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Applying Flow Proofs to Complex Geometric Problems

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:

  1. Properties of linear pairs
  2. Right angle definition
  3. Supplementary angles
  4. Congruent angles
  5. Perpendicular lines

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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying