Special Centers in Triangles

What is a circumcenter?

• A point where perpendicular bisectors intersect in a triangle

• A point where angle bisectors intersect in a triangle

• A point where medians intersect in a triangle

• A point where altitudes intersect in a triangle

What is an incenter?

• A point where perpendicular bisectors intersect in a triangle

• A point where angle bisectors intersect in a triangle

• A point where medians intersect in a triangle

• A point where altitudes intersect in a triangle

What is a orthocenter?

• A point where perpendicular bisectors intersect in a triangle

• A point where angle bisectors intersect in a triangle

• A point where medians intersect in a triangle

• A point where altitudes intersect in a triangle

The place where all three perpendicular bisectors meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Joshua is constructing a triangle with a circle inscribed in it. Each vertex of the triangle will have a line passing through it bisecting the angle. No matter where he places the third vertex, the following conditions will be true: • Each line will always bisect its corresponding vertex angle. • The three lines will always intersect at the center of the circle. • The circle will always be inscribed in the triangle. Which type of center​ (a)   exists where the three lines intersect?

• INCENTER

• CENTROID

• CIRCUMCENTER

• MIDPOINT

If S is the incenter, what type of segments are drawn?

• medians

• angle bisectors

• perpendicular bisectors

• altitudes

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

The ​ (a)   of a triangle intersect at the incenter.

• Perpendicular bisectors

• angle bisectors

• medians

• altitudes

The incenter is equidistant from the ​ (a)   and the circumcenter is equidistant from the ​ (b)   .

• sides

• vertices

• midpoints

• perpendicular bisectors

• orthocenter