Perpendicular bisector and angle bisector

Front

What is a perpendicular bisector?

Back

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

Front

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal angles.

Front

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

Back

If a point lies on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment.

Front

What is the relationship between the angles formed by an angle bisector?

Back

The angles formed by an angle bisector are equal.

Front

If point P lies on the perpendicular bisector of segment AB, what can be said about the distances PA and PB?

Back

PA = PB; point P is equidistant from points A and B.

Front

How can you determine if a point lies on the angle bisector of an angle?

Back

If the distances from the point to the sides of the angle are equal, then the point lies on the angle bisector.

Front

What is the significance of the perpendicular bisector in triangle construction?

Back

The perpendicular bisector of a side of a triangle is the locus of points equidistant from the endpoints of that side.

Front

What theorem relates to the angle bisector in a triangle?

Back

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

Front

How do you find the coordinates of the midpoint of a segment?

Back

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

Front

What is the formula for the distance between two points in a coordinate plane?

Back