Question

∆𝐀𝐁𝐂 ~ ∆𝐏𝐐𝐑. 𝐀𝐃 is the median to 𝐁𝐂 and 𝐏𝐌 is the median to 𝐐𝐑. Prove that 𝐀𝐁/𝐏𝐐 = 𝐀𝐃/𝐏𝐌.

Answer 1

Since, ΔABC ~ ΔPQR
By similarity rule, we get
AB/PQ = BC/QR
AB/PQ = 2BD/2QM (Since D and M are the mid-points of sides BC and QR respectively)
AB/PQ = BD/QM …(i)
∠𝐴𝐵𝐶 = ∠𝑃𝑄𝑅 (Similar triangles)
∠𝐴𝐵𝐷 = ∠𝑃𝑄𝑀 …(ii)
From (i) and (ii),
ΔABD ~ ΔPQM
By similarity rule, we get
AB/PQ = AD/PM
Hence, proved.