Exploring Perpendicular and Angle Bisectors in Geometry

The video tutorial covers chapter five, section one, focusing on perpendicular and angle bisectors. It begins with an introduction to perpendicular bisectors, explaining their properties and theorems, including the perpendicular bisector theorem and its converse. The tutorial then provides examples to illustrate these concepts. Following this, the video introduces angle bisectors, discussing their properties and the angle bisector theorem, along with its converse. Examples are provided to demonstrate these principles in practice. The tutorial concludes with exercises for students to practice independently.

What is a perpendicular bisector?

• A line that divides an angle into two equal parts

• A line that is perpendicular to a segment at its midpoint

• A line that is parallel to a segment

• A line that divides a segment into three equal parts

According to the perpendicular bisector theorem, what is true about any point on the perpendicular bisector?

• It is always at the midpoint of the segment

• It is equidistant from the endpoints of the segment

• It is closer to one endpoint than the other

• It is equidistant from the midpoint of the segment

In the example where line L is the perpendicular bisector of segment XY, if YW is 7.3, what is the length of XW?

• 14.6

• 7.3

• 3.65

• 10.5

If point A is equidistant from points B and C, what can be inferred about point A?

• It lies on the parallel bisector of segment BC

• It lies on the midpoint of segment BC

• It lies on the perpendicular bisector of segment BC

• It lies on the angle bisector of segment BC

What is an angle bisector?

• A line that divides a segment into three equal parts

• A line that divides an angle into two equal parts

• A line that is perpendicular to a segment at its midpoint

• A line that is parallel to a segment

According to the angle bisector theorem, what is true about any point on the angle bisector?

• It is equidistant from the vertex of the angle

• It is always at the vertex of the angle

• It is equidistant from the sides of the angle

• It is closer to one side of the angle

In the example where Ray JM bisects angle JKL, if LM is 12.8, what is the length of JM?

• 25.6

• 6.4

• 12.8

• 15.6

If point D is equidistant from Ray BA and Ray BC, what can be inferred about point D?

• It lies on the midpoint of segment BC

• It lies on the perpendicular bisector of segment BC

• It lies on the angle bisector of angle ABC

• It lies on the parallel bisector of segment BC

If angle ABC is 112 degrees and is bisected by Ray BD, what is the measure of angle ABD?

• 56 degrees

• 112 degrees

• 28 degrees

• 84 degrees

If point G is equidistant from points D and E, and the length of DE is 20.8, what is the length of DG?

• 10.4

• 20.8

• 5.2

• 15.6