Q) If AD and PM are medians of triangle ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that AB / PQ = AD / PM.


If AD and PM are medians Triangles CBSE 10th important questions

Given that,  Δ ABC ~ Δ PQR, therefore

\frac{AB}{PQ} = \frac{BC}{QR}

Since AD is median of BC, hence BC = 2BD

Similarly, PM is median of QR, hence QR = 2QM

\therefore  \frac{AB}{PQ} = \frac{2BD}{2QM}

or  \frac{AB}{PQ} = \frac{BD}{QM}

and ∠ B = ∠ Q                (given that Δ ABC ~ Δ PQR)

\therefore  Δ ABD ~ Δ PQM        (by SAS similarity)

Therefore, \frac{AB}{PQ} = \frac{AD}{PM}

Hence proved.

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top