Right angled bisector
On the screen, let us first see two points A and B. A line segment AB is drawn in black color. Now we take a free point D on the plane and line segments AD and BD are drawn we also draw a perpendicular to line segment AB from point D in red color where foot of the perpendicular is point C. Now move the points A, B and D and observe how the lengths of AC, BC, AD and BD get changed.
1. Set the point D so that AC=BC, what do we observe? 2. Set the point D so that AD=BD, what do we observe?