Senior one mathematics solid geometry examination questions.

Solution: (1) Two planes are expanded into one plane, which is a rectangular CDEF.

If FB‖AC is the diagonal of a square, then the quadrilateral ACBF is a parallelogram.

The connection of MN is MP+PN.

Since CM=BN=a,

NP‖AF and MP‖AD can be obtained,

Therefore, the plane composed of MNP is parallel to the plane composed of ADF.

That is, the AFD of MN‖ plane is proved.

(2)NP=(√2)a/2，PM= 1-(√2)a/2

mn=√[(np)^2+(mp)^2]=√{[(√2)a/2]^2+[ 1-(√2)a/2)]^2}

mn=√[a^2/2+ 1-(√2)a+a^2/2]=√[a^2+ 1-(√2)a]