Corollary to a theorem Chapter 5 (p. 227)
Theorem that states that the acute angles of a right triangle are complementary.
A corollary to a theorem is a statement that follows directly from the theorem and is often a simpler or more specific result. In other words, corollaries are the logical consequences of the already proven theorems.
For example, let’s suppose we have a theorem that states If x and y are even integers, then their sum is also an even integer. A corollary to this theorem could be If x and y are odd integers, then their sum is also an even integer. This is a logical consequence of the original theorem, as it is simply applying the same logic to a different scenario.
Corollaries are important because they help to establish deeper connections between different mathematical concepts and can often be useful in further mathematical investigations. Additionally, they can provide simpler, more specific results that are easier to apply in practical situations than the original theorem itself.
Overall, corollaries are an important part of mathematical proofs and help to build a deeper understanding of complex mathematical concepts.
More Answers:
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