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Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that triangle ABC is similar to triangle PQR.







Median divides the opposite side.

BD = BC/2 and QM = QR/2

GIven that AB/PQ = BC/QR = AD/PM

 AB/PQ = 1/2 BC / 1/2 QR = AD/PM

AB/PQ = BD/QM = AD/PM

In Triangle ABD and Triangle PQM 

AB/PQ = BD/QM = AD/PM  (Proved above)

? ?ABD ? ?PQM (By SSS similarity criterion)
? ?ABD = ?PQM (Corresponding angles of similar triangles)
In ?ABC and ?PQR,
?ABD = ?PQM (Proved above)

AB/PQ = BC/QR
? ?ABC ? ?PQR (By SAS similarity criterion)


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