Which term describes the point where the three angle bisectors of a triangle intersect?

The point where the three angle bisectors of a triangle is incentre.

Step-by-step explanation:

Let  a triangle ABC and  its three angle bisector of a triangle intersect at a point O.

The point O is called point of incentre where three angle bisector of a triangle intersects.

Incentre: Incentre is define as the point  where the three angle bisector of a triangle meet .

Properties of Incentre:

1. Centre of incircle: The incentre is the centre of the triangle's incircle , the largest circle which fir inside the triangle and touch all its three sides .

2. Always inside the a triangle: The triangle's incentre is always lie inside the triangle.Adjust the triangle  by dragging any vertex and see that it will never go outside of  the triangle.

It is possible to find the incentre of triangle by using compass and straightedge.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)