6-1 & 6-2 Entry Ticket - Perpendicular and Angle Bisectors

Front

What is the definition of the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the definition of the Circumcenter of a triangle?

Back

The Circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

What is the definition of the Centroid of a triangle?

Back

The Centroid is the point where the three medians of a triangle intersect. It is the center of mass of the triangle.

Front

What is the definition of the Orthocenter of a triangle?

Back

The Orthocenter is the point where the three altitudes of a triangle intersect.

Front

If point P is the circumcenter, which segment is equal to PB?

Back

PC

Front

How do you find the measure of an angle using the Incenter?

Back

The measure of an angle can be found using the property that the Incenter is equidistant from the sides of the triangle, allowing for the use of angle bisector theorem.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the lengths of the other two sides of the triangle.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the relationship between the incenter and the incircle?

Back

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.

Front

How can you determine the location of the circumcenter in an obtuse triangle?

Back

In an obtuse triangle, the circumcenter lies outside the triangle.