4. In APOR, PO = OR; L.M and N are themidpoints of the sides of PO, QR

1.	4. In APOR, PO = OR; L.M and N are themidpoints of the sides of PO, QR and RPrespectively. Prove that LN = MN.RHS theoremAtimit
Answer» INΔPQR ,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] PQ=QR L,MN are midpoints of PQ,QR,PR respctively ⇒PL=PQ=QM=MR.............................(i) and ∠QPR=∠QRP(angles opp. to equal sides)......................................(ii) Step-by-step explanation: in ΔLPN and Δ MNR PL=MR(from (i)) ∠LPN=∠MRN(from (ii)) PN=NR( N is midpoint) ∴ΔLPN≅ΔMNR(By SAS congruency) ⇒LN=MN(corresponding sides) Hence Proved

4. In APOR, PO = OR; L.M and N are themidpoints of the sides of PO, QR and RPrespectively. Prove that LN = MN.RHS theoremAtimit

Answer»

INΔPQR ,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]

PQ=QR

L,MN are midpoints of PQ,QR,PR respctively

⇒PL=PQ=QM=MR.............................(i)

and ∠QPR=∠QRP(angles opp. to equal sides)......................................(ii)

Step-by-step explanation:

in ΔLPN and Δ MNR

PL=MR(from (i))

∠LPN=∠MRN(from (ii))

PN=NR( N is midpoint)

∴ΔLPN≅ΔMNR(By SAS congruency)

⇒LN=MN(corresponding sides)

Hence Proved