How do you draw a right angle DEF?

Answer 1

I am guessing that you are asking for a compass-and-straight-edge construction of a right angle. Let us say that the line DE is given, and we are given a point F not on the line, and we are asked to drop a perpendicular line from F to DE. Set the compass radius large enough so that when you draw a circle centered at F, it crosses DE in 2 points, say A and B. Now draw a circle centered at A with a radius larger than AB, and a circle of the same radius centered at B. The 2 circles intersect in 2 points, one on each side of the line ABDE. Let C be the one on the opposite side of the line from F. Use the straight edge to draw the line CF. That is your perpendicular. It also bisects DE, by the way. It is known as the perpendicular bisector of DE.