Explored by:

Aubrey D. Johnson

We will investigate that whether we can create five equal segments of equal length using these two lines and a line connecting the midpoints. We will now add the midpoints of the two lines to the picture.

So now we see the midpoints of the angle, BAC. These midpoints have been labeled Y and Z. I believe that the segment, YZ will be the same length as AZ, ZC, AY and YB. We will now test this theory. Let us first construct a segment connecting the two midpoints Y and Z.

Now that we have our three lines and our five segments, we should measure AC and BC. If these lines are the same length the AY = YC = CZ = ZB = ZY.

We now see that AC = BC. So if Z is the midpoint of BC then ZC = ZB . Also If Y is the midpoint of AC then YC = YA. We have already measured ZY, so now we will see if the other four segments are the same length.

Using Geometers Sketchpad I was able to get an accurate measurement of the segments. We have created an angle with segments of equal length.