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(4 IF AD And PM are Medians of trainglesABC and pqr respectively where traingle ABC traingle pqr prove that ab=adpq=pm |
| Answer» CONSIDER the TRIANGLES △ABC and △PQRAD and PM being the mediums from vertex A and P respectively.Given : △ABC∼△PQRTo prove : PQAB = PMAD It is given that △ABC∼△PQR⇒ PQAB = QRBC = PRAC [ from the side-ratio property of similar △ s]⇒∠A=∠P,∠B=∠Q,∠C=∠R.......(A)BC=2BD;QR=2 QM [P,M being the mid points of BC q QR respectively]⇒ PQAB = 2QM2BD = PRAC ⇒ PQAB = QMBD = PRAC ........(1)Now in △ABDq△PQMPQAB = QMBP ........[ from (1)]∠B=∠Q........[ from (A)]⇒△ABD∼△PQM [ By SAS property of similar △ s] from the side property of similar △ s HENCE provedPQAB = PMAD | |