Question

In ؈ABCD, M and N are the mid-points of AD and BC. If AB || CD, prove that MN || AB.

Answer 1

Answer:

MN║CD, proved.

Step-by-step explanation:

See the diagram.

First, draw a line between D and B and this line meets MN at O point.

Now, in ΔDMO and ΔBNO,

(i) DM= BN  

This is because M and N are the midpoints of AD and BC respectively and ABCD being a parallelogram AD=BC.  

(ii) ∠ODM=∠OBN (Alternate Angle)

This is because AD║BC and DB is the connecting line.

And, (iii) ∠DOM =∠BON (Opposite angle)

So, it can be concluded that ΔDMO≅ ΔBNO.

Hence, we can write DO=OB.

Now, in ΔABD, the midpoint of AD is M and the midpoint of DB is O.

Hence, MO must be parallel to AB i.e. MO║AB.

Therefore it can be concluded that MN║AB.

(Proved)