[Ramanjaneyulu Kakumani]

2) Congruance is Equivalance Numbers

• for Any numbers N,M -- |N-N| is divisible by M  --> Reflexive ( N~ N)
• if two numbers N, P -- |N-P| is divisible by M, then |P-N| also divisible by M --> Symmetric (N~P)
• If three NumberN,P,Q -- |N-P| is divisible by M and |P-Q| is divisible by M then|N-Q| is also divisible by M -- Transitive ( N ~ P ~ Q )

Hence, Congruance of Numbers is Equivalance

[Ramanjaneyulu Kakumani]

1) Gluing point is Equivalance

• Any point can be glued to same point -- Reflexive (A~A)
• If point A is Glued to point B => Point B is glued to Point A -- Symmetric (A~ B)
• If Point A is Glued to Point , Point B is glued to Point C, means Point A is glued to C -- Transitive (A~ B, B~ C then A~ C).

Hence Gluing point on a plane is Equivalance.

2) Congruance is Equivalance

• Triangle A is congruent to Triangle A -- Reflexive (A ~ A).
• If Triangle A is congruent to Triangle B => Triangle B is congruent to Triangle A -- Symmetric (A ~ B)
• If Triangle A is congruent to Triangle B , Triangle B is congruent to Triangle C, means Triangle A is congruent to C -- Transitive (A~ B, B~ C then A~ C).

Hence Congruance is Equivalance

 

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