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.

Answer 1

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)