ASSIGNMENT 6
**BRIAN DEITZ**

# 6

### Given three points A, B, and C. Draw
a line intersecting AC in the point X and BC in the point Y such
that

**AX = XY = YB**

**In this assignment I had to use
parallel lines, points, segments and circles with center point
to construct a triangle and get AX=XY=YB. By doing this I was
able to get segments that no matter how they are changed, that
AX=XY=YB will always be true.**

**I start the assignment by constructing
a random angle with vertices A,C,B and then closed the figure
to make a triangle ACB.**

**STEP 2****: ****I constructed
a random point on segment AC and I labeled this point P. Next,
I constructed a parallel line through P that is parallel to segment
CB so I could use P as a center to make a circle that would intersect
the parallel line.**

**STEP 3****: **Construct a circle
with the center at P passing through point A. I then marked the
intersection point of the circle centered at P and the parallel
line that I constructed in Step 2. I called this point of intersection
point D.

**STEP 4****: ****After
labeling point D I constructed a second circle centered at D with
radius that is equal to the segment of DP.**

**STEP 5****: ****I then
needed to mark the point E which is the intersection of the circle
(c2) and the segment AB. I then constructed segments DE for the
purpose of finding a parallel to this segment through P.**

**STEP 6****: ****My next
construction was that parallel line that went through P and was
parallel to DE.**

**STEP 7****: I constructed point F which was the intersection
of the parallel line constructed in step 6 and the circle (c1)
that was centered at P.**

**STEP 8****: I constructed another segment FE. **

**STEP 9****: ****I constructed
line AF and marked the intersection on this line and CB as point
Y. This length will be AY in the equation.**

**STEP 10****: ****I then
constructed my third and final circle with YB as radius and center
at A Where this circle meets segment AC I labeled at point. I
now have my my AX and AY.**

**STEP 10****: ****To complete
the construction I constructed segment XY and now I have my three
segments in the construction. Let's see if these are EQUAL??**

**As you can see AX=XY=YB. You
can see all of this at work and play with the GSP construction
below.**

**View
the entire GSP construction file here!!**
**HERE
IS A GSP CONSTRUCTION OF THIS PHENOMENON**