Perpendicular bisectors and angle bisectors

Front

What is a perpendicular bisector?

Back

A line that divides a segment into two equal parts at a 90-degree angle.

Front

What is an angle bisector?

Back

A ray that divides an angle into two equal angles.

Front

How do you find the length of a segment using the perpendicular bisector?

Back

Use the midpoint formula and the distance formula to calculate the lengths.

Front

What is the relationship between perpendicular bisectors and triangles?

Back

The perpendicular bisectors of a triangle intersect at a point called the circumcenter, which is equidistant from the vertices.

Front

What is the significance of the circumcenter in a triangle?

Back

It is the center of the circumcircle, the circle that passes through all three vertices of the triangle.

Front

How do you determine if a point lies on the perpendicular bisector of a segment?

Back

A point lies on the perpendicular bisector if it is equidistant from the endpoints of the segment.

Front

What is the measure of angles formed by angle bisectors?

Back

The angle bisector divides the angle into two equal parts, so each part measures half of the original angle.

Front

How can you find the measure of an angle using its bisector?

Back

If you know the measure of the angle, divide it by 2 to find the measure of each resulting angle.

Front

What is the relationship between angle bisectors and triangles?

Back

The angle bisectors of a triangle intersect at a point called the incenter, which is equidistant from the sides of the triangle.

Front

What is the significance of the incenter in a triangle?

Back

It is the center of the incircle, the circle that is tangent to all three sides of the triangle.