SideAB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ?PQR (check image). Show that ΔABC ~ ΔPQR

Answers

• 

  Shirisha

  August 17, 2020

  Given two triangles, ΔABC and ΔPQR in which AB, BC and median AD of ΔABC are proportional to sides PQ, QR and median PM of ΔPQR

  AB/PQ = BC/QR = AD/PM

  To Prove: ΔABC ~ ΔPQR

  We have? AB/PQ = BC/QR = AD/PM (D is the mid-point of BC. M is the midpoint of QR)

  ΔABD ~ ΔPQM [SSS similarity criterion]

  Therefore, ∠ABD = ∠PQM [Corresponding angles of two similar triangles are equal]

  ∠ABC = ∠PQR

  In ΔABC and ΔPQR

  AB/PQ = BC/QR ———(i)

  ∠ABC = ∠PQR ——-(ii)

  From the above equation (i) and (ii), we get

  ΔABC ~ ΔPQR [By SAS similarity criterion]

  Comment