Given that lines ac and ge are both perpendicular to line bf, and ag and ce are both perpendicular to ge, you can conclude

That means AC and GE are parallel lines, and also AG and CE are parallel lines.

Whenever 2 lines are perpendicular, they form 90°. If the second line is perpendicular to the third line, then the third line is rotated 180° with respect to the first line (90°+90°=180°). Rotating a line 180° looks the same as rotating it 360°, because they are simetric. Rotating a line 360° is the same as not rotating it at all. The only difference is that it may be above or below, but with the same slope. When 2 lines have the same slope, they are parallel.