Math, asked by niwaneshreya04, 7 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​

Attachments:

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

Learn more;

The diagonals of a trapezium intersect at point a the ratio of the ...

https://brainly.in/question/18766598

17. A trapezium ABCD has sides AB and DC parallelA straight line ...

https://brainly.in/question/13193548

Similar questions