Question

2. Sides AB and BC and median AD of a
triangle ABC are respectively propor-
tional to sides PQ and QR and median
PM of APQR (see Fig. 6.41). Show that
A ABC - APQR.​

Answer 1

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

Answer 2

Step-by-step explanation:

In triangle ABC and triangle PQR,

AB BC AC

------ = ------ = ------ ...... ( given )

PQ QR PM

By using, Ratio of area of two traingles having sides in proportion is equal to the same ratio.

Therefore,

AB A ( ABC )

------ = --------------

PQ A ( PQR )