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Construct a Line Perpendicular to a Given Line - through a point not on the given line

Construct a Perpendicular Line - through a point not on a line

We'll start with point A, not on a line. It takes two points to make a line. I'm showing one (not named) so that we can later move it around. We need two points that are on the line that are the same length from A. Can you construct that, using point A and the one point already on the line? Label your intersections B and C. Now construct the perpendicular bisector of segment BC by making two circles with radius BC and centers at B and C. Label the intersections of those two circles as D and E. Construct line DE. Is point A on line DE? Do a drag test. That is, move all the points you are able. Does your construction stay true? Are the lines always perpendicular? Is segment BC always bisected? What kind of triangle is ABC? What can you say about line DE? What can you say about segment BC when it is combined with ANY point on line DE?

Construct a perpendicular line through a point not on the line