Question

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Answer 1

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), MNDM=BNDC 

 

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.

Answer 2

Answer:

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Step-by-step explanation:

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