The locus of a point equidistant from two fixed points A and B is known as the ___ of the line segment AB.

Perpendicular bisector

True or False: The locus of a point that is always at a fixed distance from a given point is a line.

False. The locus is a circle.

Fill in the blank: The locus of points equidistant from two intersecting lines is the ___ of the angles formed by those lines.

Angle bisector

What geometric shape is formed by the locus of points that are a constant distance r from a fixed point O?

A circle with center O and radius r

The locus of a point equidistant from two parallel lines is a line that is ___ to both lines.

Parallel

If two lines are 6 cm apart, at what distance from each line must a point be to be equidistant from both?

3 cm

A point P is equidistant from lines AB and CD. If PL is perpendicular to AB, what property does triangle POL have?

Triangle POL is a right triangle.

The locus of midpoints of equal chords in a circle is the ___ of the circle.

Circumference

In triangle ABC, if BX bisects ∠ABC and intersects AC at D, what can be concluded about point D?

D is equidistant from sides AB and BC.

What is the ratio in which the centroid divides each median of a triangle?

2:1

True or False: The circumcenter of a triangle is equidistant from the triangle's sides.

False. The circumcenter is equidistant from the triangle's vertices.

If points A and B are fixed, what geometric locus is created by all points P such that ∠APB = 90°?

The circumference of a circle with AB as the diameter.

The locus of a point at a fixed distance from a line consists of how many lines?

Two lines parallel to the given line.

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

PA is equal to PB.

What geometric figure is formed by the locus of midpoints of parallel chords in a circle?

The diameter of the circle perpendicular to the parallel chords.