Congruence statements, with a statement of percentage

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In summary, the conversation discusses three statements of congruence (x = a mod n, y = b mod m, z = c mod p) and how they relate to a given percent of the sum of x, y, and z. The question is whether this information uniquely determines or restricts the values of x, y, and z. The Chinese remainder theorem is mentioned as a possible application, but further clarification is needed.
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1MileCrash
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Suppose I have three statements of congruence:

x = a mod n, y = b mod m, z = c mod p;

Furthermore, x is a given percent of x + y + z, as is y and z.

Does this uniquely determine x, y, z? Or does it at least restrict x to a predictable subset of the congruence class of a, and so on?

Thank you.
 
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  • #3

1. What is a congruence statement?

A congruence statement is a mathematical statement that compares two geometric figures and states that they are exactly the same size and shape. It is often represented using the symbol ≅.

2. How do you write a congruence statement?

A congruence statement is written by naming the congruent parts of the two figures in the same order. For example, if two triangles have corresponding sides of equal length, the congruence statement would be written as "ΔABC ≅ ΔDEF", where A and D are corresponding vertices, B and E are corresponding vertices, and C and F are corresponding vertices.

3. What is the purpose of using congruence statements?

Congruence statements are used to prove that two geometric figures are the same size and shape. This is important in geometry because it allows us to make accurate measurements and predictions about the relationships between different shapes and figures.

4. How are congruence statements related to percent?

Congruence statements can be used to express the degree of similarity between two figures as a percentage. This is often done by calculating the ratio of the corresponding sides or angles and converting it to a percentage.

5. Can congruence statements be used for non-geometric figures?

Congruence statements are typically used in geometry, but they can also be applied to other fields, such as physics and chemistry. In these cases, congruence statements may refer to the similarity of physical or chemical properties between two objects or substances.

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