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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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
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