What is the difference between symmetry and congruence

Congruent is the precise term that is generally used for identical and geometric figures whereas similar is the term that is used to get a loose idea about the figures. The concept of congruent figures follows stringent mathematical principles and theorems whereas similar figures do not follow any such concepts. The term congruent can be used as an adjective to denote the coincidental and superimposed incidents whereas similar is used to define the experience or objects of similar nature.

Congruent is the term that refers to the figures or anything, in general, that is the same in size and shape and can superimpose each other. Similar is used for the figures or other things that resemble each other in the size and shape but are not identical to each other in terms of measurements.

Congruent figures usually follow the mathematical principle of the S. S theorem where the measurements of all sides and angles in two figures are the same. Similar or identical figures do not follow any such rule.

The shape, sides, and angles of the two figures can vary differently. Similar is the loosed term to define the identical figures that resemble each other in shape largely. Congruent figures superimpose each other even when they are placed in different orientations. However, when they are mapped or rotated they are exact replicas of each other and therefore will be congruent.

Similarity in the mathematical world requires two objects to have the same shape but not necessarily the same size. Two different circles for instance are both circles and therefore similar but their size makes them different. They can be compared as similar shapes, but not mapped to one another. Two objects that are similar will have the same shape but the one could be a scaled up or a scaled down version of the other. The orientation of the shape could be different, but they will remain similar.

Mathematically objects are similar if they have the same shape but not necessarily the same size. The dictionary describes congruent as an adjective that means agreeing or accordant. Similarity means having a likeness or resemblance and is also an adjective. The word similarity is far more widely used in day to day conversations. The word congruent is used as a synonym to the word similar but the word similar is not a fitting synonym to congruent. There are many instances where similarity is used to describe everyday things and a likeness to almost everything that you could possibly compare.

Objects can be similar, experiences could be similar, the natural world has many similarities and conversations could also be thought to be similar. Similarity is a word used in the work place and at home. Congruent is not so widely used out of mathematical or formal informative types of writing. Congruent is about matching and agreeing on ideas and principles especially in law and politics. Synonyms suggested for congruent include conforming, identical and consistent.

All of these words reflect the controlled and formal aspect of congruent. When thoughts can be coincident and superposable they are thought to be congruent. Congruence can refer to harmony and compatibility in the musical world.

The lyrics, video and view of a scene, all projecting the same theme, could be described as congruent ideals. They fit together to make the same whole idea or thought. This would be a more abstract use of the word congruent as it is perceived to show the same qualities of an idea, design or art form in unison.

Take an object. Imagine moving it and then seeing whether it looks the same before and after. Then it has symmetry. Or have two copies of a plane shape and picking one off of the other and placing it back down after moving it turning, flipping in 3-space which is the same as reflecting in the plane.

Students could play a game. One closes their eyes the other can move it so it 'looks the same afterwards' and the first student has to guess WHETHER it was moved - and how.

Also, for plane figures, you can try a mirror or MIRA to see if it looks the same before and after reflection. Testing for another symmetry. Try a ball. You cannot tell if it is rotated. If you had a mirror it looks the same before or after. Lots of symmetry. Symmetry, in general is one of the KEY ideas in all of geometry. It is used in chemistry, in physics, in engineering, in looking at images for thinking about algebra. It is, as they say, a BIG idea. Euclidean Geometry. Available Documents.

The Difference between Congruence and Equality. The Pythagorean Theorem and Pythagorean Triples. An Example of an Analysis and Proof.

Planning a Proof.