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Name Class 55 Date Indirect Proof and Inequalities in One Triangle Going Deeper Essential question: How can you use inequalities related to triangle side lengths and angle measures in proofs? Two

How to fill out indirect proof and

How to Fill Out an Indirect Proof:

1. Identify the goal: In an indirect proof, you start by assuming the opposite of what you want to prove. So, first, determine what you want to prove and clearly state it as your goal.
2. Make an assumption: To begin the indirect proof, assume the opposite of your goal is true. This assumption is called the "negation" of your goal.
3. Use deductive reasoning: Utilize deductive reasoning and logical steps to derive a contradiction from the assumption made in step 2. This may involve applying theorems, postulates, or rules of logic to the given information.
4. Reach a contradiction: Through logical steps and deductive reasoning, strive to reach a contradiction. This contradiction can be any situation that directly contradicts the assumption made in step 2.
5. State the contradiction: Clearly state the contradiction that you have derived. This contradiction demonstrates that the assumption made in step 2 is false.
6. Conclude the proof: Since the assumption made in step 2 is false, the opposite must be true. Therefore, you can conclude that your initial goal from step 1 is proven.

Who Needs Indirect Proof:

1. Mathematics students: Indirect proof is an important technique often used in advanced mathematics, particularly in the fields of algebra, geometry, and calculus. Students studying these subjects need to understand and utilize indirect proof as they encounter complex proofs and logical reasoning.
2. Mathematicians and researchers: Indirect proof is not limited to educational settings. Mathematicians and researchers use indirect proof to prove theorems, conjectures, and solve challenging problems. It allows them to approach problems from an alternative perspective and provide rigorous proofs.
3. Logical thinkers: The skill of indirect proof goes beyond mathematics. It is beneficial for individuals who enjoy critical thinking, logical reasoning, and problem-solving. The ability to prove statements indirectly can be applied in various fields, such as philosophy, computer science, and even legal argumentation.

In conclusion, learning how to fill out an indirect proof involves identifying the goal, making an assumption, using deductive reasoning, reaching a contradiction, and concluding the proof. Indirect proof is useful for mathematics students, mathematicians, researchers, and anyone who wishes to enhance their logical thinking abilities.

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What is indirect proof and?

Indirect proof is a method of proving a statement by assuming the opposite and showing that this assumption leads to a contradiction.

Who is required to file indirect proof and?

Generally, anyone who needs to prove a statement or hypothesis using indirect proof may be required to file it.

How to fill out indirect proof and?

To fill out indirect proof, one must first assume the opposite of the statement to be proven, then derive a contradiction using logical reasoning and valid arguments.

What is the purpose of indirect proof and?

The purpose of indirect proof is to prove a statement or hypothesis by showing that assuming the opposite leads to a logical contradiction.

What information must be reported on indirect proof and?

The information reported on indirect proof may include the statement to be proven, the assumption made, the logical reasoning used, and the final contradiction derived.