Online assignment - congruence and similarity

2. ONLINE SUBMISSION OF
ASSIGNMENT
CONGRUENCE AND SIMILARITY
CONCEPTS IN NATURE /
ENVIRONMENT
PREPARED BY
K.V.PADMAJA
B.Ed MATHEMATICS

3. Introduction:
“In this changing world, those who understand and can do mathematics will have
significantly enhanced prospects and options for shaping their futures. Mathematical
competence opens doors that produce opportunities. A lack of mathematical competence
keeps those doors closed. All students should have the opportunity and the support
necessary to learn mathematics with depth and understanding”
The application of Mathematics can be found all around us - in our daily lives, in the
natural environment that we live in. Studying the congruency and similarity in nature is
the aim of this assignment. The aim is to understand whether there are mathematical
concepts in nature
If you ever have to build something you'll use these principles. There are a lot of triangles
in real life applications. Scale models use these principles as well, and they're also
necessary for data extrapolation, mathematical modelling, engineering... there are many,
many applications that use these simple principles.
I shall be discussing about the same in this assignment.
Definitions:
“Congruent shapes are the same shape and size as one another, but can be in different
positions, orientations, or form mirror images”
If one shape can become another using Turns, Flips and/or Slides, then the shapes are
Congruent:
“Shapes are similar if they have the same proportions. They may have different positions
and orientations”
Two shapes are Similar when the only difference is size (and possibly the need to turn
or flip one around).

4. Congruent or Similar?
- The two shapes need to be the same size to be congruent.
- When we need to resize one shape to make it the same as the other, the shapes are
Similar
When We Then the Shapes are….
Only Rotate, Reflect and/or Translate Congruent
Also need to Re-size Similar
Whether shapes are congruent or similar can be found by comparing their internal angles
and the length of their sides.
Congruence and Similarity concepts found in Nature:
1. Leaf: In a tree all leaves will be similar. Also, when we consider one leaf, the midrib
and the lines on the two sides are same. Hence congruent
Even in a Coconut Leaf, the big leaves are equally distributed both sides and the lines
are congruent on both sides
2. Buildings: Consider Villa houses, almost all are same in area and size. We can find
proof for congruency and similarity even within one building where the alignment of pillars
etc are congruent. A few other strikingly congruent buildings are Tajmahal, Bridges,
Towers, Pyramids etc

5. 3. Insects: Butterflies, with their beautiful wing designs are an example of congruency
and similarity
There is congruency in the way their entire form is designed by nature – the whiskers, the
size and shape of both sides of its wings and the designs within them aswell.

6. 4. Fruits and Vegetables: Citrus fruits like lemons, oranges, peaches etc and Pea Pods
display congruency and similarity through the alignment of their seeds and pods.
5. Garden and Pathways are other places where we can find the mathematics of
congruency and similarity
The alignment of the trees, the way the pathways are laid are all examples to the topic of
our discussion.
6. Books – whose area, shape, size, angle, elevation etc. are perfect examples of
congruency and similarity in everyday life.
Also, when we look at poems, they have a specific methodology to making them sounding
poetic – be it Sonnets or Tirukural with the display of similarity in the arrangements of the
verses itself and the words in the first and second line

7. 7. Earrings – Its fancy how there is mathematics in everything. Consider the pairs of
earrings below. They are a perfect example of congruency and similarity
8. Automobiles – The engineering behind the development of the abutomobiles ensure
the congruency and similarity be it the tyres or the windows or many parts that make the
vehicle move

8. 9. Science – How can we not mention about the scientific “congruency and similarity”
found our own body? Our Hands, the skeletal system etc. are perfect and accurate
reflections of the topic discussed. Also, we can find congruence in similarity in the
structure of our DNA and chromosomes as well. These are merely a few examples in the
vast universe of such existence of the concept.

9. Conclusion:
Mathematics is a science that is all around us. Understanding the concepts of
mathematics will enable people handle their everyday situations and resources better.
The concept of congruence is not restricted to the study of geometry. It plays an important
role in everyday living. We may be able to buy a refill for our pen when the ink runs dry.
We use congruence to replace a worn out part of the car, looking for the 'same part
number'. In construction, they have to use the blocks of a 'standard size'. When using
screws, we look for the kind of screw that we need and also screwdriver that fits. In each
of these examples, the idea of sameness of shape and sizes applies.
After reading this assignment, the learners will be able to link the mathematical concepts
to the objects they see around in nature. They will also be able to appreciate the influence
of mathematics in their day to day life. It will also create an interest in them to know more
about the correlation of mathematics and mathematical concepts in our environment.
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