(1) From ∠ DBC = 45 and BDC = 90, it is easy to judge that △DBC is an isosceles right triangle, and BC = 2 √2 can be found from Pythagorean theorem, and then the length of EG can be found to be √2 according to the fact that the center line on the hypotenuse of the right triangle is half of the hypotenuse.

Solution: (1) In △DBC, ∠ DBC = 45, BD⊥DC (known).

△ DBC is an isosceles right triangle.

∴BD？ +DC？ =BC？ (Pythagorean theorem)

CD = 2 (known)

∴BC=2√2

In Rt△DBC, point G is the midpoint of BC edge (known).

∴ eg = 1/2bc (the midline of the hypotenuse of a right triangle is equal to half of the hypotenuse)

∴EG=√2

Let's do this first. I'm going to bed.