Question

In the adjacent figure 5.44, ABCD is a trapezium. AB||DC. Points M and N are midpoints of diagonal AC and DB respectively then prove that MN||AB.

Answer 1

Answer:

MN ║ AB

Step-by-step explanation:

Lets take mid point of BC as P & Join MP

in Δ ABC

AM = CM = AC/2  

& BP = CP/2

hence using mid point theorem

MP ║ AB

Similarly

Take mid point Q of AD & Join ND

in Δ ABD

BN = DN = BD/2

& AQ = DQ = AD/2

=>  NQ ║ AB

MP ║ NQ ║ AB

PQ ║ AB  ( as mid point of AB & DC)

=> M & N lies on PQ

=> MN ║ AB