[math]\bigtriangleup CAB[/math] is an isosceles triangle. The base is segment [i]CB[/i] and the legs are segments [i]CA [/i]and [i]BA[/i]. Segment [i]AD [/i]bisects [math]\angle CAB[/math], the vertex angle of the triangle.
Drag a vertex. What do you notice about segments CD and DB?
What can you conclude that segment AD does to segment CB?
Segment AD bisects segment CB.
What type of angles are [math]\angle CDA[/math] and [math]\angle BDA[/math]?
Write a conjecture that summarizes your findings about the angle bisector, segment AD, of the vertex angle in an isosceles triangle and its base, segment CB.
The angle bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base of the triangle.