Once you are through with elementary geometry and learn about measurements, you are all set to understand the relationships between two figures. It is when you come across terms like symmetry, parallel and intersecting lines, etc. Moving forth, you delve deeper and find a bit more interesting topics like congruence. In simple words, two figures are objects that are carbon-copy of each other are said to be congruent. When you place them one above the other, the congruent figures overlap point-to-point.
The need of learning about congruence
Learning about congruence in figures is necessary to build our understanding of structures. When you find two buildings, things, or products completely identical to each other, it is because of the spatial intelligence developed. The same intelligence helps understand the concept of congruent figures.
Also, the figures may be in different planes; still, they will be congruent when the sides, areas covered and the volume occupied are the same. This concept is useful in fields of:
- Product modeling
- Landscape designing
- B2B manufacuring
Besides practical utility, the congruence builds up the base for the learners and enables them to form a smoother understanding of the concepts of areas and volumes. Just like we read about the equality of numbers in elementary arithmetic class, we come across congruence while comparing two figures in a geometry session.
Some examples of congruent figures
I suggested some congruent games to help you with applying this concept. The idea of congruence may further amaze you when you come across things of daily utility based on it. Such practical examples tell us that congruence helps attain a level of mastery and prepares us for jobs where we apply it to meet certain objectives. Mostly, the concept of congruent figures proves its utility when multiple items of the same specifications are to be developed at a mass level. Here are a few examples:
1. Pages of a book
Imagine a book that has pages with uneven measurements. It is sure to look messy to you and will not be easy to store. Every page of the book fits inside the cover perfectly only because these are conforming to a set specification or are congruent.
2. The spokes of the Ferris wheel
All spokes of the Ferris Wheel are exactly the same size and shape. The idea of congruence in wheels helps achieve balance in this ride.
3. Pencils in a box
Pencils of the same brand are machine cut. Since all are of the same size and shape, these can be said to be congruent.
4. Nuts and bolts
Nuts and bolts are things of mass production. These are designed using pre-defined specifications as per the site of the application. Their identicality of shape and size achieved due to industry-set norms make them a classic real-life example of congruent objects.
5. Kidneys and lungs in our body
Human beings are said to be having bilaterally symmetrical body. This symmetry is known to have its impact in a few internal organs too. Kidneys and lungs are in pairs, and interestingly are identical in physical measurements. That is why these exhibit congruency.
6. Two mobile phones with the same specifications
Many times we get confused about the ownership of two mobile phones from the same brand having same specifications. These are said to be congruent to each other because of this identicality. The congruency here dictates the genuineness of the product.
7. Bangles of same size, earrings of same design
Bangles, as well as earrings, are made exactly the same so that these look beautiful and not out of place. These are molded with a pre-set die sometimes. Congruency in these items serves the purpose of imparting beauty and uniformity of looks here.
8. Various copies of book with same title
We all have copies of a book with the same title released by the same publication house. How identical they look and are of exactly the same measurements, aren’t they? It is nothing but the relationship of congruency these exhibits.
9. Billiards racks
That triangular ball holder which we see along with the billiards table is exactly the same in physical attributes. Two such racks can safely be called congruent to one another.
10. Sheets of a letter pad
Being exactly the same in size and material too, the sheets of a letter pad offer a good example of congruent shapes in daily life.
11. Tennis balls of the same brand
All tennis balls produced by the same brand follow a preset manufacturing specification giving us congruent figures to spot on a tennis court.
12. Biscuits in a pack
Congruence is everywhere; it is there in the packet of your favorite biscuits too! Each biscuit is the exact copy of the other offering you the full value of the food item per piece.
13. Two playing dice provided in a game
One interesting example of congruent figures which children can easily relate with are two dice provided in a game. Every dice is congruent to each other.
14. Carrom discs
Every carrom disc of black, white, and red color is congruent in shape to one another. It is an interesting example to tell kids about congruent figures in real life.
15. Two bricks
It is another thing of mass production. The congruency is used to make the bricks which are molded first in specific measurements and then baked to create identical building blocks.
16. Copies of a passport size photograph
When we say ‘true copy’ of photographs, the photographer swears by the perfection he puts in creating those and gives us a relatable example of congruent figures in the world around us.
17. Currency bills and coins of same denomination
Pre-defined measurements laid out by the State to mint coins and print currency bills help us tell the genuine apart from the fake one. What a meaningful use of congruency it is!
18. Post cards and inland letters
If you belong to the old school of communication, you must have stored lots of postcards and inland letters. Look at those closely and you will find an intriguing example of congruent figures in practical life.
19. Floor tiles of same company
All floor tiles produced by the same company come in specific measurements. These tiles can be called congruent to one another and help us get a well-designed space to step on.
20. Cloth Hangers of Specific Size
All cloth hangers when hung on a rod or stacked above one another provide us a harmonious sight. Their ability to overlap one another and look exactly the same comes from product modeling. It gives us another interesting illustration of congruency in things we see around us.
Congruency in figures is an interesting concept that helps us build and improve math reasoning skills. Sometimes, it forms a parameter of perfection and can be a useful element for quality checks. Even nature has blessed us with congruency by giving us internal body organs that are mirror images of each other. Once this milestone in learning shapes is achieved, the road ahead to complex geometry concepts eases a bit. If you also feel compelled to look for examples of congruence around you after reading the ones above, do come forward and enlighten me, too, with your learning.