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 $\displaystyle A$ and $\displaystyle B$.
Construct line $\displaystyle L$, parallel to $\displaystyle A$ and $\displaystyle d_1$ units from line $\displaystyle A.$
Construct line $\displaystyle M$, parallel to $\displaystyle B$ and $\displaystyle d_1$ units from line $\displaystyle B.$
They intersect at point $\displaystyle P$ which lies on the angle bisector.
Repeat the procedure with distance $\displaystyle d_2$
. . and locate point $\displaystyle Q.$
Draw the line through $\displaystyle P$ and $\displaystyle Q.$