Are Areas of Similar Circular Sections Proportional to Chord Squares?

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In summary, to start a proof, it is important to first understand the statement or problem and then state assumptions, define terms, and use logical steps and previous theorems. When choosing which axioms to use in a proof, carefully consider their relevance and applicability. A valid proof follows a logical sequence and can be checked for justification and coherence. If a counterexample is encountered, the proof may need to be revised or the statement modified. To improve proof writing skills, practice, seek feedback, and familiarize yourself with different techniques and strategies.
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Homework Statement



Show that the areas of similar circular sections are proportional to the squares on their chords. Assume that the result that the areas of circles are proportional to the squares on their dimeters.

Homework Equations



no sure

The Attempt at a Solution



What does "squares on their chords mean" and "squares on their diameters mean"? I am having trouble visualizing what this is supposed to look like.
 
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  • #2
read "squares on their chords" as "the square of the length of the chord"
 

FAQ: Are Areas of Similar Circular Sections Proportional to Chord Squares?

How do I start a proof?

To start a proof, it is important to first understand the statement or problem that you are trying to prove. Then, you can begin by stating your assumptions and defining any necessary terms. From there, you can use logical steps and previous theorems to build your proof.

How do I know which axioms to use in a proof?

Axioms are self-evident statements that are accepted as true without needing to be proven. In a proof, you can use any axioms that are applicable to the problem at hand. It is important to carefully consider which axioms are relevant and necessary for your proof.

How do I know if my proof is valid?

A valid proof follows a logical and coherent sequence of steps that lead to the conclusion you are trying to prove. It is important to check that each step is justified and that the conclusion logically follows from the given assumptions and axioms. Additionally, you can seek feedback from others to ensure the validity of your proof.

How do I handle a counterexample in a proof?

A counterexample is an example that disproves a statement. If you encounter a counterexample in your proof, it means that the statement is not universally true. You can either revise your proof to account for the counterexample or modify the statement to make it more specific.

How do I improve my proof writing skills?

Practice and feedback are key to improving your proof writing skills. It is important to regularly work on challenging problems and to seek feedback from others, such as professors or peers. Additionally, familiarizing yourself with different proof techniques and strategies can also help improve your skills.

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