Checkpoint 3.4.1.
Construct an equilateral triangle with side length matching a given segment.
Section 3.4 Constructions
For each construction figure out how to do it using the classic Greek tools: a straight edge and rusty compass (okay that isn't quite classic Greek). Note you can use the circle and line tools in Geogebra to perform these. Next prove that your construction works.
Subsection 3.4.1 Discover and Prove Construction
Checkpoint 3.4.2.
Given a line segment construct the perpendicular bisector of it.
Checkpoint 3.4.3.
Construct a square with side length matching a given segment.
Checkpoint 3.4.4.
Construct the midpoint of a line segment.
Checkpoint 3.4.5.
Construct the bisector of given angle.
Solution.
Start with segments \(\overline{AB}\) and \(\overline{BC}.\) Construct a circle centered at \(B,\) with a radius of either \(|AB|\)m> or \(|BC|,\) say \(|BC|.\) Mark where this circle intersects with \(\overline{AB}\) and call this point \(D.\) Construct \(\overline{CD}\) and then find the midpoint of this segment. We can do this by constructing two circles of radius \(|DC|\) centered at \(D\) and \(C,\) then marking where these two circles intersect, \(E\) and \(F\text{,}\) then constructing \(\overline{EF},\) and finally marking the intersection of \(\overline{CD}\) and \(\overline{EF},\) call it G. The ray from \(B\) through \(G\) is the angle bisector of angle \(ABC\) because \(G\) is equidistant from \(D\) and \(C\) since it is the midpoint of \(\overline{CD}\) and so it equally splits our original angle.
Checkpoint 3.4.6.
Copy an angle.
Checkpoint 3.4.7.
Construct a line parallel to a given line through a given point.
