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Example of a line segment is parallel to a plane

Question:

In the figure shown, P-ABCD is a pyramid. ABCD is a square. PB is perpendicular to the plane ABCD. E is midpoint of PA. F is midpoint of BC. Prove that EB is parallel to plane PDF.

Proof:

Find the midpoint in line segment PD and name this midpoint of PD as point G. Connect EG.

because E is the midpoint of PA and
G is the midpoint of PD,

This is based on the midpoint theorem. The segment joining the midpoints of two sides of a triangle is parallel to the third side and equals to half the third side.

In square ABCD,
because F is the midpoint of BC.

Here we use the property of a square, opposite sides are parallel and equal, interior angles are 90 degrees.

Because EG // AD and BF // AD, so EG // BF.
Because EG = (1/2) AD and BF = (1/2) AD, so EG = BF.
Connect GF,
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