In the given figure, PQR is a triangle in which PQ = PR. In the given figure, PQR is a triangle in which PQ = PR. QM and RN are the QM and R

Question

In the given figure, PQR is a triangle in which PQ = PR. In the given figure, PQR is a triangle in which PQ = PR. QM and RN are the QM and RN are the medians of the triangle. Prove that medians of the triangle. Prove that (i) ΔNQR ≅ ΔMRQ (ii) QM = RN please

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Sarah 2 weeks 2021-09-10T21:31:06+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-10T21:32:14+00:00

    Answer:

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    Solution:

    ΔPQR is an isosceles triangle. [∵ PQ = PR]

    ⇒ 1/2 PQ = 1/2 PR

    ⇒ NQ = MR and PN = PM

    (i) In ΔNQR and ΔMRQ

    NQ = MR (Half of equal sides)

    ∠NQR = ∠MRQ (Angles opposite to equal sides)

    QR = RQ (Common)

    ΔNQR = ΔMRQ (By SAS rule)

    (ii) QM = RN (Congruent parts of congruent triangles)

    (iii) In ΔPMQ and ΔPNR

    PN = PM (Half of equal sides)

    PR = PQ (Given)

    ∠P = ∠P (Common)

    ΔPMQ = ΔPNR (By SAS rule)

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    0
    2021-09-10T21:32:26+00:00

    Answer:

    ΔPQR is an isosceles triangle. [∵ PQ = PR]

    ⇒ 1/2 PQ = 1/2 PR

    ⇒ NQ = MR and PN = PM

    (i) In ΔNQR and ΔMRQ

    NQ = MR (Half of equal sides)

    ∠NQR = ∠MRQ (Angles opposite to equal sides)

    QR = RQ (Common)

    ΔNQR = ΔMRQ (By SAS rule)

    (ii) QM = RN (Congruent parts of congruent triangles)

    (iii) In ΔPMQ and ΔPNR

    PN = PM (Half of equal sides)

    PR = PQ (Given)

    ∠P = ∠P (Common)

    ΔPMQ = ΔPNR (By SAS rule)

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