Corollary to a theorem Chapter 5 (p. 227)
Theorem that states that the acute angles of a right triangle are complementary.
A corollary is a statement that follows immediately from a previously proven theorem, without the need for additional proof. It is a natural consequence of the theorem and is often used to extend or clarify the results of the theorem.
In Chapter 5 of a math textbook or paper, a corollary would be a statement that relates directly to a theorem proved in that chapter. For example, if the chapter introduces a theorem about the angles in a triangle and their measures, a corollary to that theorem might be a statement about the isosceles triangles and how their angles relate to each other.
Corollaries are useful tools for understanding and applying mathematical concepts. They enable us to extend the results of a theorem to related situations without having to redo the proofs. Additionally, corollaries can help to clarify the implications of theorems by presenting them in a more specific context. In summary, a corollary is a powerful tool used in mathematics to make logical deductions that build on previously proven theorems.
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