Dividing a Segment Construction
by: Maggie Hendricks
To begin our construction we should construct a circle with center X and place a point C along its circumference.
Next construct a diameter of circle X through point C by constructing the ray
. The point where the ray exits the circle should be called A.
Now construct another point along the circumference of circle X and call it Y. Using Y as a center and
as a radius, construct a new circle Y.
Construct the ray
and label the point where it exits circle Y as B.
If we hide all that was used in our construction we see the desired image below.
The argument we will now investigate is that by construction,
. See the proof below to show that this statement is valid.
since they are both radii of circle X
since they are both radii of circle Y
by the transitive property of equality
Thus,.