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Question
Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.
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Solution
In ΔABC and ΔPQR
BC = QR
AD and PM are medians of BC and QR respectively
⇒ BD = DC = QM = MR
In ΔABD and ΔPQM
AB = PQ
D = PM
BD = QM
Therefore, ΔABD ≅ ΔPQMABD PQM ...(SSS criteria)
Hence, ∠B = ∠Q
Now in ΔABC and ΔPQR
AB = PQ
BC = QR
∠B = ∠Q
Therefore, ΔABC ≅ ΔPQRABC PQR. ...(SAS criteria)
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