Ray BD is a bisector of triangle ABC because it divides the triangle into two congruent triangles, triangle ABD and triangle BDC.
According to the diagram, ray BD is a bisector of triangle ABC.
A bisector of a triangle is a line segment that divides the triangle into two congruent triangles. In other words, a bisector divides the triangle in half so that the two halves are exactly the same.
In the diagram, ray BD divides triangle ABC into two triangles, triangle ABD and triangle BDC. These two triangles are congruent, meaning that they have the same side lengths and angles.
One way to see this is to notice that angle ABD is equal to angle BDC. This is because ray BD is a bisector of angle ABC, which means that it divides angle ABC into two equal angles.
Another way to see that triangle ABD is congruent to triangle BDC is to notice that the two triangles have a common side, BC. They also have two sides that are congruent (AB and BD), and two angles that are congruent (ABD and BDC).
Therefore, we can conclude that ray BD is a bisector of triangle ABC.