Difference Between Equal And Congruent

Congruent vs Equal

Congruent and equal are similar concepts in geometry, but ofttimes misused and confused.

Equal

Equal means that the magnitudes or sizes of any two in comparison are the same. The concept of equality is a familiar concept in our day to mean solar day lives; however, as a mathematical concept information technology has to exist defined using stricter measures. Different field uses a different definition for the equality. In mathematical logic, it is defined using Paeno`s Axioms. Equality refers to the numbers; often numbers representing backdrop.

In the context of geometry, the equality has the same implications equally in the common usage of the term equal. It says that if the attributes of two geometrical figures are the same and then the two figures are equal. For example, the area of a triangle can be equal to the surface area of a foursquare. Here, simply the size of the property 'surface area' is concerned, and they are the aforementioned. Simply the figures themselves cannot be considered as the same.

Coinciding

In the context of geometry, congruent means equal in both figures (shape) and sizes. Or in simpler words, if one tin exist considered equally an exact copy of the other then the objects are congruent, irrespective of the positioning. It is the equivalent concept of equality used in geometry. In the case of congruence besides much stricter definitions are provided in belittling geometry.

Regardless of the orientation of the triangles show above they tin exist positioned so that they perfectly overlap each other. Hence they are equal in both size and shape. Hence they are congruent triangles. A effigy and its mirror image are also congruent. (They can be overlapped after rotating them around an axis lying in the plane of the shape).

In the above, even though the figures are mirror images, they are congruent.

Congruence in triangles is important in the study of plane geometry. For two triangles to exist coinciding, the corresponding angles and the sides are to be equal. Triangles can be considered coinciding if following conditions are satisfied.

• SSS (Side Side Side)  if all three respective sides are equal in length.

• SAS (Side Angle Side)  A pair of corresponding sides and the included angle are equal.

• ASA (Bending Side Angle)  A pair of corresponding angles and the included side are equal.

• AAS (Bending Angle Side)  A pair of corresponding angles and a non-included side are equal.

• HS (hypotenuse leg of a right triangle)  Two correct triangles are coinciding if the hypotenuse and one side are equal.

The case AAA (Angle Angle Angle) is Non a case where congruence is always valid. For instance following two triangles have equal angles, but non coinciding considering the sizes of the sides are different.

What is the divergence betwixt Congruent and Equal?

• If some attributes of geometric figures are the same in magnitude, and so they are said to be equal.

• If both the sizes and the figures are equal, then the figures are said to be congruent.

• Equality concerns the magnitude (numbers) while congruence concerns both the shape and the size of a figure.

Difference Between Equal And Congruent,

Source: https://www.differencebetween.com/difference-between-congruent-and-vs-equal/

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