Definition of Congruence
In mathematics, congruence refers to the relationship between two geometric figures or values that have the same shape and size
In mathematics, congruence refers to the relationship between two geometric figures or values that have the same shape and size. In other words, if two objects or values are congruent, it means they are exactly the same in terms of their measurements and characteristics.
When we talk about congruence in two-dimensional geometry, we typically refer to congruent figures or shapes. Two polygons are considered congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure.
In more formal terms, the definition of congruence for two polygons is as follows:
Two polygons P and Q are congruent if and only if:
1. Their corresponding sides are equal in length. This means that if side AB of polygon P is congruent to side CD of polygon Q, and so on for each pair of corresponding sides.
2. Their corresponding angles are equal in measure. This means that if angle ∠A of polygon P is congruent to angle ∠C of polygon Q, and so on for each pair of corresponding angles.
Congruence can also be applied to other geometric objects, such as triangles, circles, and rectangles. For example, two triangles are congruent if their corresponding sides and angles are equal.
In addition to two-dimensional shapes, congruence can also be discussed in the context of numbers. In number theory, congruence refers to the relationship between two integers that have the same remainder when divided by a certain integer. For example, if two numbers leave the same remainder when divided by 5, we say they are congruent modulo 5.
Overall, congruence is a fundamental concept in mathematics that allows us to identify and compare objects or values that are essentially equivalent in terms of their shape, size, or characteristics.
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