# 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!!