How would I draw an equilateral triangle with three lines in it forming six right angles?

Assuming you know the length of each of the three given lines (and all three lines are of equal length), this is not a difficult construction. First draw any line, then draw a line segment perpendicular to the first line. On that line segment, measure off the given line length. At the end of the line segment, use a protractor to form 30° angles on either side of the line segment. Extend the new lines to intersect the first line you drew. This will complete an equilateral triangle. (Each of the other two given lines will bisect one of the other angles and be perpendicular to the opposite side.)