Hello, MATNTRNG!
Imagine a sheet of paper with two lines drawn on it, as shown.
Without extending the paper or the lines, construct the bisector
of the angle determined by the two lines. Code:
*
*
*
* .
* .
* . d1
* . L
* . o
A * o
o
o
o o o ♠ o o o M
o P .
o .
o .
. d1
.
.
B * * * * * * * * *
Given two nonparallel line segments
and
.
Construct line
, parallel to
and
units from line 
Construct line
, parallel to
and
units from line 
They intersect at point
which lies on the angle bisector.
Repeat the procedure with distance 
. . and locate point 
Draw the line through
and 