Question

ab is parallel to dc m is midpoint of ad and n is midpoint of bc if ab is 5.7 and mn is 6.2 find dc
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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, QBBD=QNDC

2=QNDC (Q is the mid point of BD)

QN=21DC

Similarly, QM=21AB

Hence, QM+QN=21(AB+DC)

MN=21(AB+CD)

Hence, MN=21(11+8) = 9.5 cm