In the given figure, PQR is a triangle in which PQ = PR. QM and RN are the medians of the triangle. Prove that
a) ∆NQR ≅ ∆MRQ
b) QM = RN
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Answers
Answered by
14
Step-by-step explanation:
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)
Answered by
2
Step-by-step explanation:
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