JKLM is a trapezium where JK || ML. If the diagonals MK and JL intersect each other at N, then the value of MK × NL is always equal to
Answers
Given : JKLM is a trapezium where JK || ML. If the diagonals MK and JL intersect each other at N,
To Find : value of MK × NL is always equal to
Solution:
Comparing
ΔMNL with ΔKNJ
∠MNL = ∠KNJ ( vertically opposite angles)
∠NML = ∠NKJ ( alternate interior angles)
∠NLM = ∠NJK ( alternate interior angles)
=> ΔMNL ≈ ΔKNJ (AAA Similarity criteria)
=> MN/KN = NL/NJ
=> NL * NK = MN * NJ
=> NL * ( MK - MN) = MN * NJ
=> NL * MK - NL * MN = MN * NJ
=> NL * MK = MN * NJ + MN * NL
=> NL * MK = MN ( NJ + NL )
=> NL * MK = MN ( JL)
=> NL * MK = MN * JL
=> MK * NL = MN * JL
MK * NL = MN * JL
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