M is a point on the side of BC of a parallelogram ABCD DM and produced meets every produced at and prove that DM i m n is equal to DC IBN and DNA by DM is equal to a Android DC
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M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that
(i) DM/MN=DC/BN
(ii) DN/DM=AN/DC
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ANSWER
M is a point on the side BC of a parallelogram ABCD
(i) Consdier △DMC and △NMB,
∠DCM=∠NBM alternate angles
∠DMC=∠NMB vertically opposite angles
∠CDM=∠MNB alternate angles
By AAA-similarity:
△DMC∼△NMB
From similarity of the triangle:
MN
DM
=
BN
DC
(ii)
From (i),
MN
DM
=
BN
DC
Add 1 on both sides
MN
DM
+1=
BN
DC
+1
MN
(DM+MN)
=
BN
(DC+BN)
Since AB=CD
MN
(DM+MN)
=
BN
(AB+BN)
DM
DN
=
DC
AN
Hence proved
Step-by-step explanation:
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