Question

What are Congruences?

Answer 1

Hint: In order to answer the question, first we will discuss the exact definition of Congruence and then we will discuss how congruence is differ from equal. And, we will also discuss how congruence is crucial in the field of geometry.

Complete step by step solution:
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. All the more officially, two arrangements of focuses are called compatible if, and just in the event that, one can be changed into the other by an isometry, i.e., a blend of unbending movements, specifically an interpretation, a turn, and a reflection. This implies that either item can be repositioned and reflected (however not resized) in order to agree decisively with the other article. So two unmistakable plane figures on a bit of paper are compatible on the off chance that we can remove them and, at that point, coordinate them up totally. Turning the paper over is allowed.
In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.
$ * $ Two line segments are congruent if they have the same length.
$ * $ Two angles are congruent if they have the same measure.
$ * $ Two circles are congruent if they have the same diameter.
In this sense, two plane figures are compatible suggests that their relating qualities are "consistent" or "equivalent" including their comparing sides and points, yet additionally their comparing diagonals, edges, and territories.

Note: - If two numbers and have the property that their difference is integrally divisible by a number (i.e., is an integer), then and are said to be "congruent modulo.
 In fact, any integer which is congruent to either 4 or 9 mod 10 is also a solution.