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12/07/2021 12:01 pm
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Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see Figure). Show that:
(i) ΔABM ΔPQN
(ii) ΔABC ΔPQR
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12/07/2021 12:03 pm
Given parameters are:
AB = PQ,
BC = QR and
AM = PN
(i) 1/2 BC = BM and 1/2 QR = QN (Since AM and PN are medians)
BC = QR
1/2 BC = 1/2 QR
⇒ BM = QN
In ΔABM and ΔPQN,
AM = PN and AB = PQ (As given in the question)
BM = QN (Already proved)
∴ ΔABM ΔPQN by SSS congruency.
(ii) In ΔABC and ΔPQR,
AB = PQ and BC = QR (As given in the question)
ABC = PQR (by CPCT)
So, ΔABC ΔPQR by SAS congruency.