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In ∆ABC and ∆PQR, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. Prove that ∆ABC ≅ ∆PQR.
"
Given:
AB = PQ, BC = QR
CB and RQ are extended to X and Y respectively
∠ABX = ∠PQY
To prove: Here we have to prove that ∆ABC ≅ ∆PQR.
Solution:
∠ABC $+$ ∠ABX = 180 (Straight angle) ....(i)
∠PQR $+$ ∠PQY = 180 (Straight angle) ....(ii)
From (i) and (ii):
∠ABC $+$ ∠ABX = ∠PQR $+$ ∠PQY
Given that, ∠ABX = ∠PQY
∠ABC = ∠PQR ....(iii)
Now, in ∆ABC and ∆PQR:
AB = PQ (Given)
∠ABC = ∠PQR (from eq. iii)
BC = QR (Given)
So, ∆ABC ≅ ∆PQR by SAS criteria.
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