Geometry introduces us to shapes and figures. Delving deeper into this subject, we learn to find relationships among figures. The similarity is one of the concepts that may fascinate geometry beginners or young learners. Understanding this concept may prove easier for children when they can relate to it in a more practical manner. What to include in a learning-oriented lesson plan to teach the concept of similar figures? Often, teachers and parents find themselves in fix trying to ease the learning woes for kids. They try several options; giving real-life examples is one of them.
Solving geometry problems using manipulatives that require children to find length, width, or height based on the concept of similarity is one way of acquiring this skill. The same practice can be translated into real-life situations to solve a few functional problems.
How the idea of similarity is applied in real-life
Similar figures have the same shape but they may differ in size. Unlike congruent figures which are exact copies of each other, similar figures can be said to be proportionate to each other. The similarity concept is applied in real-life to measure the height and distance of the building, river, or angles.
The idea of similarity can help simplify complex problems one needs to solve in real-life situations. For example, if you wish to find the height of a building, you need not climb it all the way up. You can simply do the same by measuring its shadow and comparing it with the shadow of an object of a similar structure.
Similarly, trigonometry principles coupled with the idea of similarity help in estimating the width of a river. The shadow of a ship’s mast making an angle with the bank of the river gives us a right triangle. By applying the similarity of angle’s principle, the user can estimate the width of the river. It allows estimating the length of the bridge required for solving the transportation problem.
In a few lines of work such as architecture, computer-aided modeling, and infrastructure development, the idea of similarity goes into making the models of a proposed building. When the model is correct and emerges from in-depth knowledge of similarity, scaling it up to a full-fledged structure becomes a smooth and seamless process. Hence, building model’s visualization using synonymity and difference is one of the key areas where the idea of similarity provides ample support.
Keeping these facts in mind, we’ve listed here a few of the striking examples of similar figures that you can see around in real life.
Common examples of similar figures
1. A rectangular TV screen and the rectangular dining table top
Though quite unrelated to each other, these two surfaces enjoy the relationship of similarity with one another. If you are searching for some examples of rectangular shapes around, these two offer an interesting combination. The similar rectangles differ only on the lengths of the sides, which is interestingly presented in these similar figures.
2. A pole and a pencil
Pole and pencil are similar to each other in shape. They both are cylindrical and the former looks like a vertically stretched version of this item of stationery. These objects are examples of cylindrical shapes that are of common occurrence. So, whenever you think of cylindrical figures in real-life, look no further than that lamp-post outside your house and in your pencil box. Paper-towel tubes, Rolling pins, and straight staws are other cylindrical shapes we can locate in our daily life.
3. An egg and an oval mirror
While one is a food item and the other a home decor material, they both are oval in shape and look similar to one another. These shapes also serve the purpose right when you are searching for ellipsoid figures around you. Oval is another term that is used to describe a person’s face shape. Hence, real-life examples of oval shapes are quite interesting and can drive you to explore the world around you more deeply.
4. A dice and a room
If you look closely, a room is a magnified version of a dice that you use to play board games. The room and dice are examples of cubes in real life. We also have ice cubes, Rubik’s cube, boxes for rings to go to when you need to locate cubic figures in your surroundings. Cubes are 3D presentations of squares and can be cut equally along two axes of symmetry. These objects can help you have a quick demonstration material to explain this figure to young learners.
5. A clock dial and a Pizza
A clock dial and a Pizza are examples of circular shapes that we can locate around us. Circles have got no sides, but these have the circumference, area, radius, diameter, etc. that can help measure this figure from various perspectives. Explaining the relevance of these can become easy by helping children locate circular shapes like clock dial and pizza. Other circular figures worth talking about are merry-go-round from the top, Roulette table, circular dining tabletop, etc. when you want to show similar circular figures in real life.
6. Chessboard and square-tiled floor
Chessboard and a square-tiled floor resemble each other a lot and make a perfect pair of square-shaped figures available around. Other similar figures are – keyboard keys and computer monitors, square rubber stamps, square billboards and nameplates, and so on. The children can absorb the idea of similarity of figures of squarish shapes by referring to these objects that they commonly encounter at home, schools, and other places.
7. Mobile phone and calculator
Both mobile phones and calculators look so similar to each other that one may get confused between them if not noticed attentively. These make another pair of real-life similar figures based on a rectangle shape. An interesting activity to do with these objects is measuring their sides using a ruler. The kids can grasp the idea of proportional sides, which is one of the main criteria to define similarity in figures.
8. A few pentagons around us
Pentagon building, black portions of a football, traffic crossing signs are some pentagons we see around us in real life. When you propel kids into learning about polygons, the next step after quadrilateral is pentagons. The concept of figures with fives sides can prove its relevance when you show these figures to kids from the surroundings.
9. Open umbrellas and poker tables
If you look at these closely, you can appreciate these as tangible examples of octagons available around us. Octagons are eight-sided figures. These may look a lot more complicated through definitions and theoretical explanations. However, one simple mention of similar figures based on octagon shape from the surroundings can ease all learning woes. Which octagons could you locate apart from the poker table and open umbrellas?
10. A few conical shapes examples
Funnel, Christmas tree, and Waffle ice-cream cones look similar to each other and offer us examples of similar conical figures in real life. Cones have a circular base and a triangular top if looked at in a 2D plane. If you delve deeper into nature around us, you may stumble upon several conical shapes. For example, pine tree forests are full of conical canopies and offer a beautiful sight.
11. Cuboidal shapes
Rectangular packing boxes, cheese, and butter blocks, bricks, and cereal boxes are cuboidal or rectangular prism figures which are appreciable as similar shapes in our daily life. Cuboids are rectangular counterparts of cubes. To clear all confusions among cubes and cuboids, the real-life examples offer tangible support. You may ask kids to collect the pictures of cuboidal figures they find in their room and discuss in class. Such activity-based sessions help understand the practical relevance of the geometrical figures and related concepts.
Shapes build the tangible world around us. While the difference in shapes and size bring variety, the similarities offer harmony in structures fitting the space around us. Paying attention to similar figures around us can be a good start for understanding geometry and its use in real-life. The knowledge of shapes of similar structures helps further in careers like product modeling, designing, architecture, and infrastructural development.
- Papasterevski, D. (2020). Architectural Term: Self – Similarity. South East European Journal of Architecture and Design, 2020, 1–4. https://doi.org/10.3889/seejad.2020.10054
- Sheikholharam, Ehsan. (2014). Synonymity in Architecture. The Similarity of Forms and a Theory of Design. 10.13140/2.1.2993.9528.