Clearly angle AFE is 45, so triangle AEF is isosceles, with AE = AF.

From here, because AE = AF (we just mentioned it) and AB = AD (sides of a square), we can say that
==> AB - AE = AD - AF (obviously)
==> BE = DF (sides are equal)

The above will be very crucial as a proof for the congruency.

In triangles CEB and CFD,

1. Length BE = Length DF (it's needed now) [S]
2. EBC = FDC = 90 degrees (because these are angles of square) [A}
3. BC = DC (because these are sides of square) [S]

And therefore, we have the requisite Side-Angle-Side (SAS) proof needed to conclude that these triangles are congruent.

Consequently, due to the congruency, we can say that EC = FC, so triangle CEF is an isosceles triangle (using the values 10 m and 3 m, we can easily see that triangle CEF is not going to be equilateral at all).

during exam if we were to say AEF = AFE = 45degrees, do we have to give a reason as they did not tell us that the bases of that triangle is the same? or can we just state that both angles are 45degree without specifying how we got to that conclusion

Of course you have to justify them. The angles can be equal to each other because of any of the following.

1. They are given to be equal.
2. They are calculated to be equal (you saw that 180 - 90 - 45 = 45 which equals to the other 45, so this is an example of a calculated angle)
3. They are part of shapes with fixed angles (eg equilateral triangle has all 60, square has all 90)

thx :)