Exploring Perpendicular and Angle Bisectors

This video tutorial covers the concepts of perpendicular and angle bisectors in geometry. It begins with definitions and examples of each type of bisector, followed by explanations of the perpendicular bisector theorem and its converse. The video includes example problems to demonstrate how to apply these theorems in solving for unknown values. The angle bisector theorem and its converse are also discussed, with additional example problems to reinforce understanding. Students are encouraged to pause and solve problems independently to enhance learning.

What is a perpendicular bisector?

• A line that divides an angle into two equal parts

• A line that divides a segment into two equal parts and is perpendicular to the segment

• A line that is parallel to a segment

• A line that intersects a segment at any angle

What does the perpendicular bisector theorem state?

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

• If a point lies on a segment, it is equidistant from the midpoint of the segment

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

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

If 7x + 24 = 13x - 48, what is the value of x?

• x = 10

• x = 8

• x = 12

• x = 6

What is the length of RS if 7x - 22 = 4x + 5 and x = 9?

• 36

• 41

• 39

• 45

What is an angle bisector?

• A line that is perpendicular to a segment

• A line that divides a segment into two equal parts

• A line that intersects a segment at any angle

• A line that divides an angle into two equal parts

What does the angle bisector theorem state?

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

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

• If a point is on the angle bisector, it is equidistant from the midpoint of the segment

• If a point is on the exterior of an angle, it is on the angle bisector

If 4x + 30 = 9x - 5, what is the value of x?

• x = 5

• x = 6

• x = 8

• x = 7

If 13x - 4 = 8x + 11, what is the value of x?

• x = 5

• x = 4

• x = 3

• x = 2

What is the length of AD if 13x - 4 = 8x + 11 and x = 3?

• 25

• 30

• 20

• 35

If two angles are congruent and the segments are perpendicular, what can we assume?

• The segments are equal

• The angles are supplementary

• The line is an angle bisector

• The segments are parallel