Question

What is the first step in the construction of a line perpendicular to AB←→ and passing through an external point M? Assume that the construction uses only a compass and a straightedge

Answer 1

Draw a line from point M passing through AB←→, and mark the point of intersection With a compass, you cannot draw a segment. You draw arcs. So,

first do this: Place the compass needle on M and, keeping the compass width the same, draw two arcs that intersect AB From C and D, I swung two arc of the same width. Where they intersect is the second point needed to go with M to determine the perpendicular line Place the compass needle on M and, keeping the compass width the same, draw two arcs that intersect AB