Question 12:
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.
Answer:
Median divides the opposite side.
⇒ ∠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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