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Find out the detailed explanation of the final 1 question of Liaoyang mathematics senior high school entrance examination.
The original title should be AB=BC= 1/2CD.

(1) ne = MB and NE⊥MB.

(2) established.

Proof: Connect AE and extend the intersection of NE and BM at point F. 。

∫E is the midpoint of CD, AB = BC = 12cd,

Ab = European community.

And ∵AB∨CD,

That is AB∨? CE。

A quadrilateral is a parallelogram.

∫∠C = 90,

∴ Quadrilateral ABCE is a rectangle.

ab = BC,

A quadrilateral is a square.

∴ AE=AB。

In the isosceles right triangle AMN,

∴ AN=AM,∠NAM=90。

∴ ∠ 1+∠2=90 .

∵∠ 2+∠ 3 = 90,

∴ ∠ 1=∠3.

∴△nae?△mab。

∴ NE=MB,∠AEN=∠ABM。

∴ ∠4=∠6.

∵ ∠5=∠6,

∴ ∠4=∠5.

∠∠EMF =∠BMC,

∴ ∠EFB=∠C=90。

∴ BM⊥NE.