# Show that the relation R defined in the set A of all triangles as R = {(T1 , T2 ) : T1 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?

**Solution:**

R = {(T_{1}, T_{2}) : T_{1} is similar to T_{2}}

R is reflexive since every triangle is similar to itself.

If (T_{1}, T_{2}) ∈ R, then T1 is similar to T_{2}.

T_{2} is similar to T_{1}.

⇒ (T_{2}, T_{1}) ∈ R

∴ R is symmetric.

(T_{1}, T_{2}), (T_{2}, T_{3}) ∈ R

T_{1} is similar toT_{2} and T_{2} is similar to T_{3}.

∴ T_{1} is similar to T_{3}.

⇒ (T_{1}, T_{3}) ∈ R

∴ R is transitive.

3/6 = 4/8 = 5/10 = (1/2)

∴ Corresponding sides of triangles T_{1} and T_{3} are in the same ratio.

Triangle T_{1} is similar to triangle T_{3}.

Hence, T_{1} is related to T_{3}

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 12

## Show that the relation R defined in the set A of all triangles as R = {(T1, T2 ) : T1 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?

**Summary:**

Here we have observed that T_{1} is similar toT_{2} and T_{2} is similar to T_{3 }therefore T_{1} is similar to T_{3}. Hence the given relation is an equivalence relation

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