Question

In trapezium LMNO, side LO || side MN,

AN= 2LA, AM = 20A, then prove that,

MN= 2 LO.
​

Answer 1

Step-by-step explanation:

Join BD, let BD and MN meet at Q. Since, M is the mid point of AD and N is the mid point of BC. So by mid point theorem, AB II MN IICD

In △, BDC and BQN,

∠B=∠B (Common)

∠BDC=∠BQN (Corresponding angles of parallel lines)

∠BCD=∠BNQ (Corresponding angles of parallel lines)

thus, △BDC∼△BQN

Thus,

QB

BD

=

QN

DC

2=

QN

DC

(Q is the mid point of BD)

QN=

2

1

DC

Similarly, QM=

2

1

AB

Hence, QM+QN=

2

1

(AB+DC)

MN=

2

1

(AB+CD)

Hence, MN=

2

1

(11+8) = 9.5 cm