Exploring Perpendicular and Angle Bisectors

What does the term 'equidistant' mean?

• A point that is on the same line as two objects

• A point that is the same distance from two or more objects

• A point that is farthest from all objects

• A point that is closer to one object than another

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, what can be concluded?

• The point is closer to one endpoint of the segment

• The point is equidistant from the endpoints of the segment

• The point is on the segment itself

• The point is not related to the segment

What is the converse of the perpendicular bisector theorem?

• If a point is on the segment, it is equidistant from the endpoints

• If a point is not on the perpendicular bisector, it is not equidistant from the endpoints

• If a point is equidistant from the endpoints, it is on the perpendicular bisector

• If a point is on the perpendicular bisector, it is equidistant from the endpoints

What does the term 'locus' refer to in geometry?

• A point that is equidistant from two objects

• A line that intersects a segment

• A set of points that satisfies a given condition

• A single point that satisfies a condition

In the example where NP is the perpendicular bisector of LM, if LN is 2.6, what is the length of MN?

• 5.2

• 3.9

• 2.6

• 1.3

According to the angle bisector theorem, if a point is on the bisector of an angle, what can be concluded?

• The point is closer to one side of the angle

• The point is equidistant from the sides of the angle

• The point is not related to the angle

• The point is on the angle itself

If the measure of angle EFG is 50° and EF is the angle bisector, what is the measure of angle EFH?

• 100°

• 75°

• 50°

• 25°

Given that Ray YW bisects angle XYZ and WZ is 3.05, what is the distance from W to X?

• 4.57

• 3.05

• 6.10

• 1.52

What is the first step in finding the equation of the perpendicular bisector of a segment?

• Graph the line segment

• Find the midpoint of the segment

• Find the slope of the segment

• Determine the length of the segment

If the slope of a segment is 3/2, what is the slope of its perpendicular bisector?

• -2/3

• -3/2

• 2/3

• 3/2