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NCERT Class 12 · Ch 1 Exercise 1.1 · Q12

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 12

On all triangles, T₁RT₂ iff T₁ is similar to T₂. Prove equivalence. Which of triangles with sides (3,4,5),(5,12,13),(6,8,10) are related?

💡 Concept Hints

  1. Compare corresponding sides after sorting each triple by length.
  2. Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.

✅ Step-by-Step Solution

Final Answer: T₁ and T₃ are related; T₂ is not related to either. Every triangle is related to itself.
  1. Every triangle is similar to itself, giving reflexivity.
  2. Similarity is reversible. If the scale from T₁ to T₂ is k>0, the reverse scale is 1/k, giving symmetry.
  3. Successive similarity scales multiply, preserving all corresponding angle equalities and side proportions; hence transitivity.
  4. (6,8,10)=2(3,4,5), so T₁∼T₃. The ordered side ratios for (5,12,13) against either are not constant, so T₂ is not similar to them.

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