Question

5. The figure, given below, shows a trapezium ABCD. M and N are the mid-points of the non-parallel sides AD and BC respectively. Find : MN if AB=11cm and DC=8cm​

Answer 1

Answer:

MEDIUM

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ANSWER

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, 2×15=23+CD

CD=30−23=7cm