Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

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

Front

Define angle bisector.

Back

An angle bisector is a line or ray that divides an angle into two equal 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 of the triangle.

Front

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

Back

To find the length of a segment using the perpendicular bisector, measure the distance from the midpoint to either endpoint and multiply by 2.

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 two angles are bisected, what can be said about the resulting angles?

Back

The resulting angles are equal in measure.

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 formula for finding the midpoint of a segment?

Back

The midpoint M of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the relationship between angle bisectors and triangle areas?

Back

The angle bisector of a triangle divides it into two smaller triangles with equal areas if the triangles share a common vertex.

Front

How can you find the length of an angle bisector in a triangle?

Back

The length of an angle bisector can be found using the formula: l = (2ab)/(a+b) * cos(C/2), where a and b are the lengths of the sides adjacent to the angle and C is the angle.