Q12 of 65 Page 138

Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.

Median divides the opposite side

BD = and,


QM =


Given:



=



In ΔABD and ΔPQM,



ΔABD ΔPQM (By SSS similarity)


∠ABD = ∠PQM (Corresponding angles of similar triangles)


In ΔABC and ΔPQR,


∠ABD = ∠PQM (Proved above)



ΔABC ΔPQR (By SAS similarity)


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(i)


(ii) Δ DCB ~ Δ HGE


(iii) Δ DCA ~ Δ HGF

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Sides AB and AC and median AD of atriangle ABC are respectivelyproportional to sides PQ and PR andmedian PM of another triangle PQR.

Show that Δ ABC ~ Δ PQR