Q) In the given figure, CM and RN are respectively the medians of △ABC and △PQR.

If △ABC ∼ △PQR, then prove that: (i) Δ AMC ∼ Δ PNR  (ii) Δ CMB ∼ Δ RNQ.

(Q32 B – 30/1/3 – CBSE 2026 Question Paper)

Ans: It is given that:

1. CM is median of Δ ABC
2. RN is median of Δ PQR
3. Δ ABC ∼ Δ PQR

(i) Δ AMC ∼ Δ PNR:

Step 1:  ∵ CM is the median  ∴  AB = 2 AM

Similarly, ∵ RN is the median  ∴  PQ = 2 PN

Step 2: Since Δ ABC ∼ Δ PQR

∴ =

∴ =

∴ =

∴ Δ AMC ∼ Δ PNR ….. Hence proved !

(ii) Δ CMB ∼ Δ RNQ:

Step 3:  ∵ CM is the median  ∴  AB = 2 BM

Similarly, ∵ RN is the median  ∴  PQ = 2 QN

Step 4: Since Δ ABC ∼ Δ PQR

∴ =

∴ =

∴ =

∴ Δ CMB ∼ Δ RNQ: ….. Hence proved !

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