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Asked: 2023-03-28T03:46:34+00:00 In:

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of Δ PQR (see Figure). Show that: (i) Δ ABM ≅ Δ PQN (ii) Δ ABC ≅ Δ PQR

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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 Δ PQR (see Figure). Show that: (i) Δ ABM ≅ Δ PQN (ii) Δ ABC ≅ Δ PQR

Use the SAS (Side-Angle-Side) congruence.
Define the congruent to angle.
NCERT Books for Session 2023-2024, CBSE Board and Others state Board.
9th Maths EXERCISE 7.3, Page No:128, Questions No:3.

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    1. Best Answer
      Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of Δ PQR (see Figure). Show that: (i) Δ ABM ≅ Δ PQN (ii) Δ ABC ≅ Δ PQR

      (i) Given that : BC = QR
      ⇒ 1/2 BC = 1/2QR ⇒ BM = QN [∵ AM and PM are medians]
      In ΔABM and ΔPQN,
      AB = PQ [∵ Given]
      AM = PN [∵ Given]
      BM = QN [∵ Proved above]
      Hence, ΔABM ≅ ΔPQN [∵ SSS Congruency Rule]

      (ii) In ΔABM ≅ ΔPQN, [∵ Proved above]
      ∠B = ∠Q [∵ CPCT]
      In ΔABC and ΔPQR,
      AB = PQ [∵ Given]
      ∠B = ∠Q [∵ Proved above]
      BC = QR [∵ Given]
      Hence, ΔABC ≅ ΔPQR [∵ SAS Congruency Rule]

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