how do you write a paragraph proof
https://www.sparknotes.com/math/geometry3/geometricproofs/section1/
Writing a paragraph proof involves presenting a logical argument to prove a statement or theorem. Here's a step-by-step guide on how to write a paragraph proof:
1. Understand the given statement or theorem: Start by reading the statement or theorem you need to prove. Make sure you understand what it is asking for and any given conditions or assumptions.
2. Identify the information: Identify the given information, such as any given conditions, previously proven theorems, or definitions that are relevant to the proof.
3. State what needs to be proven: Clearly state what you need to prove based on the given statement or theorem. This becomes your goal for the paragraph proof.
4. Create a logical argument: Develop a logical argument that connects the given information to the desired conclusion. You may need to use definitions, previously proven theorems, or logical reasoning.
5. Provide a clear structure: Organize your paragraph proof by clearly stating each step or reason in a logical order. Use appropriate transition words, such as "because," "therefore," or "since," to connect your statements.
6. Justify each step: Provide a justification or reason for each step or statement you make in the proof. This could be based on a definition, postulate, theorem, or logical inference.
7. Use precise language: Use precise and concise language when explaining each step. Avoid vague or ambiguous statements, and ensure that your explanations are clear and easy to understand.
8. Include diagrams or illustrations (if necessary): If the proof involves geometric figures, consider including labeled diagrams or illustrations to support your explanation. However, always remember to provide a written explanation alongside any diagrams.
9. Review and revise: Once you have completed your paragraph proof, review it to ensure that each step is logically supported and that the proof is clear and coherent. Make any necessary revisions or clarifications.
Remember, writing a paragraph proof requires clear logical reasoning and a thorough understanding of the given statement or theorem. Practice and familiarize yourself with various proof techniques, such as direct proofs, indirect proofs, or proofs by contradiction, to become more comfortable with writing paragraph proofs.