Question 3:
Two sides AB and BC and median AM of one triangle ABC are respectively equal to
sides PQ and QR and median PN of ∆PQR (see the given figure). Show that:
(i) ∆ABM ≅ ∆PQN
(ii) ∆ABC ≅ ∆PQR
Answer:
(i) In ∆ABC, AM is the median to BC.
In ∆PQR, PN is the median to QR.
However, BC = QR .
BM = QN … (1)
In ∆ABM and ∆PQN,
AB = PQ (Given)
BM = QN [From equation (1)]
AM = PN (Given)
∆ABM ≅ ∆PQN (SSS congruence rule)
∠ABM = ∠PQN (By CPCT)
∠ABC = ∠PQR … (2)
(ii) In ∆ABC and ∆PQR,
AB = PQ (Given)
∠ABC = ∠PQR [From equation (2)]
BC = QR (Given)
∆ABC ≅ ∆PQR (By SAS congruence rule)
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