Use compass and ruler to draw on paper the construction described in the app below.
The following app is the same as the previous one, but now includes GeoGebra tools.
Explore the entire construction in the app above, then use the GeoGebra tools to measure lengths and angles and verify the construction numerically.[br][br](Use the [i]Undo [/i]and [i]Redo [/i]buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).
Draw the segments [math]AD,BD,BC[/math] and [math]AC[/math] in the app above or on paper, then use the GeoGebra tools or a ruler to measure their lengths.[br]Which polygon do you obtain?
Describe the properties of the obtained polygon, examining in particular the relationships between the lengths of the sides, the measures of the angles and the mutual position of the diagonals.
Based on your considerations above, explain why [math]M[/math] is the midpoint of [math]AB[/math].
When constructing the midpoint and the perpendicular bisector, we have drawn the two circles centered at the endpoints of the segment and radii equal to the segment's length.[br][br]In your opinion, is the choice of the radius length unique?[br][br]If it is not unique, explain what is the minimum compass opening (relative to the segment's length) that allows you to graphically obtain the midpoint and the perpendicular bisector of the segment.
Explain why the segment [math]CD[/math] is perpendicular to [math]AB[/math].
Find the missing word in the following sentence:[br][br]Since the segment [math]CD[/math] is perpendicular to [math]AB[/math] and passes through its midpoint, we can say that the line [math]CD[/math] is the ______________________ of segment [math]AB[/math].