In this blog entry, I will be talking about the basics of constructions, my favorite construction, and how to do it. Before I get started, there are some key terms that I will use to describe constructions that I will define below. 

- Straightedge: a ruler with no markings, used in drawing straight lines 

- Compass: a geometric tool used to draw circles and arcs 

- Arc: a part of a circle

Firstly, what is a construction? A construction is using a straightedge and a compass to draw a geometric figure. There are a lot steps a person must follow during a construction, and they must be very precise with measurements. However, if you follow the directions carefully, you'll find that doing them correctly will be easy. Some things that constructions are useful in creating are congruent line segments, congruent angles, perpendicular bisectors, angle bisectors, and many more things. 

My favorite construction is creating the perpendicular bisector of a line segment. A perpendicular bisector is a line that intersects another line at its exact midpoint, and creates angles that are perfectly right angles. I find this one pretty cool because though the steps seem difficult, it's really not hard. I also like it because it's quicker than most of the other constructions. This is mainly because the new line you're creating doesn't have to be a specific measurement, as long as it bisects the new line. Now that I've told you what my favorite construction is, it's only fair that I explain how to do it. 

How to construct the perpendicular bisector of a line segment: 

- Step One: Place your compass on one of the endpoints on the line segment. 

- Step Two: Adjust the compass so that it is more than half of the line segment's total length. 

- Step Three: Without changing the compass size, hold the compass on one endpoint and draw an arc above the line that is close to directly above the center of the line. Then draw another arc below the line that is close to directly below the center of the line. 

- Step Four: Without changing the size of the compass, move so that it's on the opposite endpoint. Repeat the process described in step three. Draw these new arcs so that the arcs above the line intersect and the arcs on the bottom intersect.  

- Step Five: The arcs on either side of the line should intersect. Where they do, draw a point.

- Step Six: Using a straightedge, connect the two points you've drawn at the intersection of the arcs. This will give you a straight line that is the perpendicular bisector of the line segment. You can now truthfully say that all angles that are created with this bisector have a measure of 90 degrees, and that line you created intersects the original line segment at its midpoint. 

Resources that helped me on this post: 

- Mathopenref.com

- Prentice Hall Mathematics Geometry book

I hope that this post on constructions has been helpful for you! Comment below for feedback.