Question

if AD and PM are medians of triangle ABC and PQR, respectively where ABC similar triangle PQR, prove that AB/PQ=AD/PM

Answer 1

we have , triangle ABC similar to triangle PQR,
since, AD and PM are medians of triangle ABC and PQR respectively.
therefore, 2AD²=AB and 2PM²=PQ.
NOW, it is also given that triangle's ABC similar to PQR
therefore, AB/PQ=AC/PR=BC/QR.
now putting the value of AB and PQ we get
2AD/2PM=AB/PQ
therefore, AD/PM= AB/PQ