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Question
In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.
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Solution
Given: AB = PQ ; BC = QR ; AD = PS
To prove: ΔABC ≅ ΔPQR
Proof:
BC = QR
2 BD = 2 QS
BD = QS ...(i)
In Δ ABD and Δ PQS
AB = PQ ...[Given]
BD = QS ...[From equation (i)]
AD = PS ...[Given]
∴ ΔABD ≅ ΔPQS ...[by SSS rule]
Then, ∠B = ∠Q ...[by CPCTC] ...(ii)
In ΔABC and ΔPQR
AB = PQ ...[Given]
∠B = ∠Q ...[ii]
BC = QR ...[Given]
∴ ΔABC ≅ ΔPQR ...[by SAS rule]
Hence proved.
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