Question

In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.

Answer 1

In ΔABC and ΔPQR and
AB = PQ
BC = QR
∠ABX + ∠ABC
= ∠PQY + ∠PQR
= 180°
∠ABX = ∠PQY
⇒ ∠ABC = ∠PQR
Therefore,
ΔABC ≅ΔPQR   ....(SAS criteria).