In geometry, a shape such as a polygon can be translated moved , rotated, and flipped over without losing its property this is referred to as rigid motion —the distances of its vertices and lengths of its sides remain unchanged. Initial analysis of the two figures above may lead you to conclude that they are not congruent since if point G of the figure at the right is made to coincide with point B of the figure at the left, the other points will not coincide.
The fact is, the two figures are symmetric or one is a mirror image of the other. To show that they are actually congruent, the figure at the right must be rotated and flipped over. Note: The figures above, except Fig. If not, click the figure; a page opens in a new tab.
In some cases, it is used as an adjective to specifically describe the objects or experiences that are superimposed or coincidental. It can also define the motivational or intrinsically linked ideals and principles of people. Similar is the loose term that is used to define the figures that look identical in shape and size. These kinds of figures do not superimpose each other because they are not to equal dimensions to each other. Thus, these figures do not produce replicas of each other.
Similar figures do not follow any mathematical concepts or principles because they are exactly not equal in dimensions or shape. These figures can be used for comparison purposes or to get just a rough idea about the shapes and sizes. It is used as an adjective to compare or to link objects or experiences of a similar nature. The similarity is not the precise concept but helps the person to get a brief hint of the principles and ideals when linked together.
Congruent and similar are the terms of the mathematical and the geometric arena. These are usually used in the concepts of precision and measurements. 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.
The antonyms suggested for congruence include inharmonious and disagreeable which further suggests that to be congruent, outside of mathematical circles, one needs to be totally in tune with the thoughts and ideals and principles that are being implemented.
Due to its formal attributes and mathematical structure congruent is not used as much in day to day conversation. Similarities are found often in the way we speak, and the word is used in numerous situations because it is more open-ended and adaptable. Similarities are found in instances where comparing two objects could be very closely compared, for instance Siamese twins would be very similar and definitely appear to be identical.
Similarities will be corresponding in their meaning like synonyms as they have a similar aspects and purpose. Synonyms are useful words that contribute to the diversity of our language and descriptions of people places and things. Similarities can relate to nature and have a natural connection in their surroundings. Leaves on the same tree for example would be similar but could be different colours in autumn.
Objects that are akin to one another are similar in quantity and character. Groups of objects or classes of animals can be similar. Cats for example are all cats, but their breed and colour and habitat would make them similar in different ways, but not the same and never congruent.
In the mathematical field of specific numbers and geometric figures the term congruent is used with precision and set measurements. The figures are accurate and although the placing of the congruent object may appear to be different, the object itself is never different but always exactly the same.
It may appear to be different to the eye initially because of the way it is positioned in space, but when it is measured specifically it is always exact. The comparison of objects that are similar is more open to description and therefore similarities are found not only mathematically, but in everyday conversations.
Making similar descriptions of objects and experiences help us to understand the world around us, people, places and things that can be similar or described as having similarities. Reading quotes like these is helpful in understanding that similarities are more variable and resonate better in the field of literature and conversation.
However, congruency, applied to motivational quotes has a way of pin-pointing the attitudes and personal changes that can be applied to life. Stephen Covey, well known speaker and author, writes about personal congruence. It comes from living a life of integrity in which out daily habits reflect our deepest values. In a sense, one copy is congruent to the other - while some of the vertices etc. So an isosceles triangle has 'symmetry' because you could pick up a copy, flip it around the central line, and put it back down onto itself.
Or - you could fold it and one side would drop down on the other as you suggested. Take a paralellogram. You probably can't fold it over like a mirror. However you CAN pick it up, turn it degrees half turn and put it back down.
That is also a rigid motion and is a symmetry. In a carefull study of patterns, we work with general combinations: translations if things are seen as infinite - going on forever , rotations, translations and combinations of these. I would primarily start working on these ideas with manipulatives, including paper folding, objects like blocks of wood, etc. Take to things.
See if one can be moved to take the place of the other. Then they are congruent. Take an object. Imagine moving it and then seeing whether it looks the same before and after. Then it has symmetry.
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