Bisector the angles between the two given straight lines.
On the screen, we see two straight lines AB and CD in black color. We have drawn angle bisectors of these two lines in blue color. We took a free point F on this coordinate plane and drew perpendiculars (FH & FG) from this point F to the lines AB and CD. We know that the distance between a point and a line is the height of the perpendicular drawn from the point to the line thus FH and FG are the distances from this point F to the two lines. Now let us move the points A, B, C, D and F and observe how the length of the perpendiculars changes.
What do you observe when this point F lies on the angle bisectors (blue)?