triangles

Construction: Extend the median AD to a point E such that AD = DE

                     Extend the median PM to a point N such that PM = N

In DEC & ABD

AD/DE= BD/DC ....................(Given)

ADB = EDC..................(Vertically opposite angles)

DEC ABD         (BY SAS)..........(1)

Similarly, PQM MNR..............(2)

DEC = ABD & QPM = MNR       (by cpct)

Now In AEC & PNR

AB = DE & PQ = NR ( from eqn 1 & 2)

AC/PR = AE/PN= EC/NR

AEC PNR    (By SSS)

DAC = MPR (cpct).........(3)

CED = RNP (cpct)...........(4)

⇒ABD =PQM

  BAC = QPR ( from 3 &4)

In ABC & PQR

AB/PQ = AC/PR

ABC  PQR (By SAS)