Question

Sides BC and AB and median AD of a ABC are
respectively proportion to side PQ & Q R & median of a
PQR. Then show that ABC similar to PQR​

Answer 1

Given: ΔABC and ΔPQR, AB, BC and median AD of ΔABC are proportional to sides PQ, QR and median PM of ΔPQR

i.e., AB/PQ = BC/QR = AD/PM

To Prove: ΔABC ~ ΔPQR

Proof: AB/PQ = BC/QR = AD/PM



⇒ AB/PQ = BC/QR = AD/PM (D is the mid-point of BC. M is the mid point of QR)

⇒ ΔABD ~ ΔPQM [SSS similarity criterion]

∴ ∠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 equation (i) and (ii), we get

ΔABC ~ ΔPQR [By SAS similarity