Answer:
Let
A be the set of all triangle in a plane.
R
= {T1, T2} : T1 is similar to T2}
i.e.
R = {T1, T2} : T1 ~ T2}
Reflexive
: Since every triangle is similar to itself.
R is
reflexive.
Symmetric
: Let (T1, T2)
is similar to
T2.
is similar to
T1.
is symmetric.
Transitive :
Let (T1, T2)
and
(T2, T3)
is similar to
T2 and T2 is similar to T3
is similar to
R is
transitive.
Hence R is an
equivalence relation.
As
triangles T1
and T3 are similar.
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