Question

Fig. 12.22
2. In a

PQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Prove that the medians of an equilateral triangle are equal.​

Answer 1

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Step-by-step explanation:

IN ΔPQR ,PQ=QR...GIVEN

∴∠R=∠P     [ANGLES OPPOSITE EQUAL SIDES]

⇒1/2 PQ=1/2 QR

⇒PL=MR

IN ΔMRN AND ΔLPN

PL=MR

∠R=∠P

PN = NR     [N IS THE MIDPOINT OF PR]

∴ΔMRN≅ΔLPN  [SAS]

⇒MN=LN     [C.P.C.T]