Exploring Perpendicular and Angle Bisectors

What does it mean for two lines to be perpendicular?

• They do not intersect.

• They intersect to form acute angles.

• They intersect to form obtuse angles.

• They intersect to form right angles.

What is a bisector?

• A line that intersects another line at an angle.

• A line that divides a segment into two equal parts.

• A line that runs parallel to another line.

• A line that intersects a segment at its midpoint.

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, it is:

• Equidistant from the endpoints of the segment.

• Not related to the endpoints.

• Closer to one endpoint than the other.

• At the midpoint of the segment.

What is the converse of the perpendicular bisector theorem?

• If a point is on the perpendicular bisector of a segment, it is at the midpoint.

• If a point is on the perpendicular bisector of a segment, it is closer to one endpoint.

• If a point is equidistant from the endpoints of a segment, it is at the midpoint.

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

If BD is a perpendicular bisector of segment AC, and AD = 4x and CD = 6x - 10, what is the value of x?

• 5

• 2

• 15

• 10

Where should a t-shirt stand be placed to be equidistant from two points?

• On the perpendicular bisector of the segment joining the two points.

• At one of the endpoints of the segment.

• At the midpoint of the segment joining the two points.

• Anywhere on the segment joining the two points.

What does an angle bisector do?

• Divides an angle into two congruent angles.

• Intersects the angle at its vertex.

• Divides a segment into two congruent segments.

• Forms a right angle with the segment.

According to the angle bisector theorem, if a point is on the bisector of an angle, it is:

• Not related to the sides of the angle.

• Equidistant from the sides of the angle.

• Closer to one side of the angle.

• At the vertex of the angle.

What is the converse of the angle bisector theorem?

• If a point is on the bisector of an angle, it is at the vertex.

• If a point is equidistant from the sides of an angle, it is at the vertex.

• If a point is on the bisector of an angle, it is closer to one side.

• If a point is equidistant from the sides of an angle, it lies on the bisector of the angle.

If RM = 7x and RP = 2x + 25, and RM = RP, what is the value of x?

• 3

• 4

• 6

• 5