Question

Two sides AB and BC and median AM triangle ABC are respectively equal to sides PQ and QR and median PN of APQR Show that: (i) AABM = APQN (ii) AABC = APQR ​

Answer 1

Answer:

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Given:

AM is the median of ∆ABC & PN is the median of ∆PQR.

AB = PQ, BC = QR & AM = PN

To Show:

(i) ΔABM ≅ ΔPQN

(ii) ΔABC ≅ ΔPQR

Proof:

Since AM & PN is the median of ∆ABC

(i) 1/2 BC = BM &

1/2QR = QN

(AM and PN are median)

Now,

BC = QR. (given)

⇒ 1/2 BC = 1/2QR

(Divide both sides by 2)

⇒ BM = QN

In ΔABM and ΔPQN,

AM = PN (Given)

AB = PQ (Given)

BM = QN (Proved above)

Therefore,

ΔABM ≅ ΔPQN

(by SSS congruence rule)

∠B = ∠Q (CPCT)

(ii) In ΔABC & ΔPQR,

AB = PQ (Given)

∠B = ∠Q(proved above in part i)

BC = QR (Given)

Therefore,

ΔABC ≅ ΔPQR

Hope this will help you....