Math, asked by niwaneshreya04, 8 months ago

JKLM is a trapezium where JK II ML. If the diagonals MK and JL intersect each other at N, then the value of MK x NL is always equal to​

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Answers

Answered by amitnrw
3

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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