Standing on the Shoulders of Giants
Here is a line m and a point C not on the line. Use straightedge and compass tools to construct a line perpendicular to line m that goes through point C.
Submit your reasoning for the actions taken and try to justify your results.
Are you ready for more?
- The line segment AB has a length of 1 unit. Construct its perpendicular bisector and draw the point where this line intersects our original segment AB. How far is this new point from A?
- We now have 3 points drawn. Use a pair of points to construct a new perpendicular bisector that has not been drawn yet and label its intersection with segment AB. How far is this new point from A?
- If you repeat this process of drawing new perpendicular bisectors and considering how far your point is from A, what can you say about all the distances?