# 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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