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Here, we learned how to construct a line through a point perpendicular to a line . Intuitively, we know that if is the reflection of a point across a line , then , just by symmetry. Therefore, construct a line perpendicular to through , and let that line intersect at . Note: is called the "projection of onto ," or the "foot of the perpendicular from to ." Finally, draw a circle centered at through with your compass, and this circle intersects line again at .
Is it intuitive?