Q6 of 70 Page 131

In Δ ABC, Δ PQR and ΔXYZ correspondences ABC ↔ PQR, PQR ↔ XYZ are similarity. Prove that ABC ↔ XYZ is similarity.

Given:- In Δ ABC, Δ PQR and ΔXYZ correspondences ABC ↔ PQR, PQR ↔ XYZ are similarity

To Prove:- ABC ↔ XYZ is similarity


Proof:- In ΔABC and ΔPQR , the correspondence ABC ↔ PQR is a similarity


∴ ∠A ≅ ∠P, ∠ B ≅ ∠Q , ∠C ≅ ∠R ………..1


…………………..eq(2)


In Δ PQR and ΔXYZ , the correspondence PQR ↔ XYZ is a similarity


∴ ∠ P ≅∠X , ∠ Q ≅ ∠Y , ∠R≅ ∠Z………………3


……………………………………..4


From 1 and 3 , we get


∠A ≅ ∠x, ∠ B ≅ ∠Y , ∠C ≅ ∠Z


Multiplying 2 and 4, we get




Thus for the correspondence ABC ↔ XYZ between ΔABC and ΔXYZ, the corresponding angles are congruent and the lengths of corresponding sides are in proportion.


∴ the correspondence ABC ↔ XYZ between ΔABC and ΔXYZ is a similarity.


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