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Angle Bisector in an Isosceles Triangle

is an isosceles triangle. The base is segment CB and the legs are segments CA and BA. Segment AD bisects , 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?

What type of angles are and ?

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.