How do we construct an angle bisector?

10.26.12

1. Create an angle ABC(any size, any degree) 

2. Put the sharp end of your compasses at point B. Draw an arc that intersects both sides of the angle. This makes one point on each side of the angle. 


3. Draw an arc from each of these points so that the arcs intersect.

4. Draw the ray from the vertex of the angle to the intersection of the two arcs drawn on the last step.










So we just did all of this:










http://www.shmoop.com/basic-geometry/angles.html
http://planetmath.org/CompassAndStraightedgeConstructionOfAngleBisector.html
http://www.ck12.org/concept/Congruent-Angles-and-Angle-Bisectors---Intermediate/r2/
http://mathforum.org/sanders/geometry/GP05Constructions.html

HOW TO CONSTRUCT A 30 DEGREE ANGLE USING JUST A COMPASS AND A STRAIGHTEDGE? 

How do we construct the basic geometric figures?

The geometric figure that were constructing is an equilateral triangle.
We are making  an equilateral triangle with a compass.

1. Start with the line segment. 
2. Put the needle of your compass at A and draw an arc.
3. Put the needle of your compass at B and draw an arc.
4. Draw the segments from the two endpoints to the point where the two arcs intersects.     

  

You should end with this :

• http://strader.cehd.tamu.edu/Mathematics/Geometry/PolygonLesson/Details/line_segment.html
• http://www.astarmathsandphysics.com/gcse_maths_notes/gcse_maths_notes_constructing_an_equilateral_triangle_60_degree_angle.html

HOW DO WE CONSTRUCT AN ISOSCELES TRIANGLE?

How do we use special segments in triangles?

The special segments we use are the median, angle bisector, and altitude. Median: connects the vertex of an angle to the midpoint of the opposite side. Angle Bisector: bisects angle in half, creating two congruent angles. Altitude: the height of a triangle. meets the "ground" at a right angle. 

Median: 








Angle Bisector:

                 


Altitude: 




http://www.atlantic.k12.ia.us/~period5/Units/Triangles/specilsegmntsoftriangles.htm

http://en.wikipedia.org/wiki/Angle_bisector_theorem