Question

special lines and points in triangles
lesson 1: centers of a triangle
fill in the blanks with either \incenter\ or \circumcenter\ to complete the state correctly.

1. the point where the triangles three angle bisectors intersect is called the
2. the point where the three perpendicular bisectors of the triangles sides intersect called the
3. the is a point that is the same distance from all three sides of the triangle.
4. the is a point that is the same distance from all three vertices of the triangle.

Explanation:

• For question 4: By definition, the intersection of a triangle's three angle bisectors is the incenter.
• For question 5: According to the definition, the intersection of the three perpendicular bisectors of a triangle's sides is the circumcenter.
• For question 6: The incenter is equidistant from all three sides of the triangle.
• For question 7: The circumcenter is equidistant from all three vertices of the triangle.

Answer:

1. incenter
2. circumcenter
3. incenter
4. circumcenter