Question

If AD and PM are medians of triangles ∆ABC and ∆PQR respectively, where ∆ABC ~ ∆PQR. prove that \(\frac{AB}{PQ} = \frac{AD}{PM}\)

Answer 1

Data : AD and PM are medians of triangles ∆ABC and ∆PQR respectively. ∆ABC ~ ∆PQR. 

To Prove:\(\frac{AB}{PQ} = \frac{AD}{PM}\)

∆ABC ~ ∆PQR.(data)

∴ we have

\(\frac{AB}{PQ} = \frac{AC}{PR} = \frac{BC}{QR}\)

D is the mid-point of BC. BD = DC. 

M Is the mid-point of QR. QM = MR

∴ \(\frac{BC}{QR} = \frac{BD}{QM}\)

In ∆ABD and ∆PQM, we have