What is congruence?
Congruence (symbol: ≅) is the
state achieved by coming together, the state of agreement. The
Latin meaning of the word congruĊ is “I meet together, I agree”. As an abstract term, Congruence means similarity between objects. Congruence, as opposed to
approximation, is a relation which implies a species of equivalence.
History of Congruence
Euclid’s Elements, Book I, was largely about
deductively developing the familiar properties of
congruent triangles, but surprisingly, Euclid never
developed a notion of congruence of triangles like
the one we use today. Instead, he considered
triangles to be “equal” if one could be positioned
directly atop another so that all their parts
(vertices and edges) coincided, a notion we call
superposition, so that their areas were equal.
CONGRUENCE IN NATURE
CONGRUENCE in daily life
Two Fifty Paise coins, Two notebooks of the same
length, Two Maps of the same scale, Two bangles, Two stamp postages on
postcards, Two boxes, Two Mats of the same length, Two window panes of the same
measurement, Two doors of the same size, A Pyramids' sides. And so on...
However, if you walk over a highway bridge, designed by
an engineer, or ride in a car or train or plane or seek surgery at the
nearest hospital or even walk into such a building as an hospital or hotel or
school or public building: you may then have reason to be glad that somebody
knows about congruent triangles, so that the building may not collapse over
your head or the bridge may not collapse under your feet or so that the miracle
medical machine they use on you at the hospital may not fry you to a crisp or
make you glow in the dark. But perhaps you are able to lead your entire life
without ever doing any of these things.
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. 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.
To strengthen rectangle add supports
that form triangles at the rectangle’s corners or across its diagonal
length. A single support between two
diagonal corners greatly strengthens a rectangle by turning it into two
triangles.
CONGRUENce in GEOMETRY
In geometry, two figures or objects are congruent if they have the same shape and size, or if one is the mirror image of the another.
•Congruent sides have the exact same length.
•Congruent angles have the same measure.
•For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.
•RECTANGLE : Two rectangles are congruent if they have the same length and breadth.
•SQUARE : Two squares are congruent if they have the same side length.
•CIRCLE : Two circles are congruent if they have the same radius .
•LINE SEGMENT : Two line segments are congruent if they have the same length.
ANGLES : Two angles are congruent if they have the same measure.
Triangles: Two triangles are congruent if the pairs of corresponding sides and corresponding angles are equal.
•Case 1: SSS congruence – If 3 sides of triangle are equal to the three sides of other triangle.
•Case 2: SAS congruence – If two sides and the included angle of one triangle are equal to the two sides and an included angle of another triangle.
•Case 3: ASA congruence – If the two angles and included side of one triangle are equal to the two angles and included side of the other triangle.
•Case 4: RHS congruence – Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.
Our Team
Standing(left to right): ANSH BATHLA, AGNIVA BAGCHI, PUSHKAR KWATRA, TANVI BENIWAL, MUSKAN GAUBA, PALKI SACHDEVA, Tiya Arora
Sitting (LEFT TO RIGHT): AMAN CHUTANI, Arindam Rao, Tanveer Singh
OUR TEAM at work
