Question

24. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that Δ ABC ~ Δ PQR.

Answer 1

Answer:

Answer:

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

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]

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

ΔABC ~ ΔPQR [By SAS similarity criterion]

Hence Proved