# What would the statement of this theorem be?

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In summary, a theorem is a proven statement or proposition in mathematics or science, while an axiom is an accepted principle. The purpose of a theorem is to establish a fundamental truth in a specific field and it is proven through a logical and rigorous process. While a theorem can be disproven, it is typically considered a fundamental truth once accepted by the scientific community.

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Given: Triangle ABC
Angle A = Angle B = Angle C

Conclusion: Line Segment AB = AC =BC

Given:Triangle ABC
Line Segment AB = AC = BC

Conclusion : Angle A = Angle B = Angle C

"If the three angles of a triangle are equal, then the three sides are equal, and conversely."

## 1. What is a theorem?

A theorem is a statement or proposition that has been proven to be true through a logical and rigorous mathematical or scientific process.

## 2. How is a theorem different from an axiom?

An axiom is a statement or principle that is accepted as true without needing to be proven, while a theorem is a statement that is proven to be true based on previously accepted axioms or other theorems.

## 3. What is the purpose of a theorem?

The purpose of a theorem is to establish a fundamental truth or relationship within a specific field of study, such as mathematics or science. It serves as a building block for further research and understanding in that field.

## 4. How is a theorem proven?

A theorem is proven through a logical and rigorous process of deduction, using accepted axioms and previously proven theorems. This process may involve mathematical equations, scientific experiments, or other methods of observation and analysis.

## 5. Can a theorem ever be disproven?

Yes, a theorem can be disproven if it is found to be inconsistent with accepted principles or if new evidence or research contradicts its conclusions. However, once a theorem has been thoroughly tested and accepted by the scientific community, it is typically considered a fundamental truth that is not easily disproven.