Question -
Answer -
Given, ╬ФABC ~ ╬ФPQR
We know that the corresponding sides ofsimilar triangles are in proportion.
тИ┤AB/PQ = AC/PR = BC/QRтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАж(i)
Also, тИаA = тИаP, тИаB = тИаQ, тИаC = тИаR тАжтАжтАжтАж.тАж..(ii)
Since AD and PM are medians, they will divide their opposite sides.
тИ┤ BD = BC/2 and QM = QR/2 тАжтАжтАжтАжтАж..тАжтАжтАжтАж.(iii)
From equations┬а(i)┬аand┬а(iii), we get
AB/PQ = BD/QM┬атАжтАжтАжтАжтАжтАжтАжтАжтАж.(iv)
In ╬ФABD and ╬ФPQM,
From equation (ii), we have
тИаB = тИаQ
From equation┬а(iv), we have,
AB/PQ = BD/QM
тИ┤ ╬ФABD ~ ╬ФPQM (SAS similarity criterion)
тЗТAB/PQ = BD/QM = AD/PM