Exploring Perpendicular and Angle Bisectors

What does the perpendicular bisector theorem state?

• Any point on the bisector is equidistant from the endpoints.

• The bisector divides the angle into two equal parts.

• The bisector is always parallel to the segment.

• The bisector is always longer than the segment.

What is the converse of the perpendicular bisector theorem?

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

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

• If a point is equidistant from the endpoints, it lies on the angle bisector.

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

In the example problem, what is the value of y when solving for the length of QR?

• 4

• 5

• 3

• 2

What is the final length of QR in the example problem?

• 22

• 18

• 32

• 10

What does an angle bisector do?

• Divides a segment into two equal parts.

• Divides an angle into two equal parts.

• Creates a right angle with the segment.

• Creates a parallel line to the segment.

In the angle bisector theorem, what is true about the perpendicular segments from the bisector to the sides of the angle?

• They are equidistant.

• They are parallel.

• They are longer than the sides of the angle.

• They are shorter than the sides of the angle.

In the example problem, what is the value of x when solving for the length of FB?

• 2

• 4

• 3

• 5

What is the final length of FB in the example problem?

• 24

• 15

• 18

• 21

What is the relationship between the segments SP and SR in the angle bisector theorem?

• They are longer than the sides of the angle.

• They are equidistant from the angle bisector.

• They are parallel to each other.

• They are perpendicular to each other.

What is the purpose of using algebra in the example problems?

• To find the midpoint of the segment.

• To prove the theorem.

• To create a new segment.

• To find the unknown variable and solve for the segment length.