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 congruent angles.

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

How do you find the length of a segment using the midpoint?

Back

The length of a segment can be found by doubling the distance from the midpoint to one endpoint.

Front

What is the significance of the circumcenter in a triangle?

Back

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

Front

If a point lies on the angle bisector, what can be said about its distances to the sides of the angle?

Back

The distances from the point to the sides of the angle are equal.

Front

What is the formula for finding the length of a segment given its endpoints?

Back

Length = √((x2 - x1)² + (y2 - y1)²) where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Front

What is the median of a triangle?

Back

A segment that connects a vertex to the midpoint of the opposite side.

Front

How do you determine if a line is a perpendicular bisector?

Back

A line is a perpendicular bisector if it is perpendicular to a segment and passes through its midpoint.

Front

What is the relationship between angle bisectors and triangle areas?

Back

The angle bisector divides the triangle into two smaller triangles with equal areas.