Hello! This is my first blog entry! This entry will be about constructions!

Constructions are creating angles, lines, segments, bisectors, and other geometric concepts using compasses and straightedges. By making a series of arcs, circles, and lines, you can make all sorts of things from equilateral triangles, to angle and line bisectors. 

My favorite construction is making and angle bisector. I like this one the best because the steps are so simple, but what you are actually doing should be impossible without the use of a ruler or a protractor. I also like finding an angle bisector because it seems incredible that someone figured out how to do this without any measuring system what so ever! 

Well, I told you my favorite construction, so I guess I'll let you know how to do it. 

1. Draw any angle (It may help to draw one with an easy/even measurement).

2. Placing the center of your compass on the angle vertex, make an arc of any length that intersects both rays of the angle. Where the arc intersects with the rays, make points.

3. From one of the points you just made, make another arc that is in between the two rays.

4. From the other new point, make an ark using the same measurement in #3 that intersects the other arc you made in #3. 

5. From the intersection of the 2 arcs, make a straight line (using a straight edge) that goes through both the angle vertex, and the intersection of the arcs. 

Well there you have it! You can now construct a bisector of an angle without the use of a protractor or ruler! COOL! 

--Joe