is similar to
T2}, is equivalence relation. Consider three right angle triangles T1
with sides 3, 4, 5. T2 with sides 5, 12, 13 and T3 with
sides 6, 8, 10. Which triangles among T1, T2 and T3
are related ?
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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