Exploring Perpendicular and Angle Bisectors

This video tutorial covers the concepts of perpendicular and angle bisectors in geometry. It explains the theorems associated with these bisectors, including how points on a perpendicular bisector are equidistant from the segment's endpoints and how points on an angle bisector are equidistant from the sides of the angle. The video also demonstrates how to find the equation of a perpendicular bisector using the midpoint and slope. Key vocabulary includes equidistant, perpendicular bisector, and angle bisector.

What is the definition of a perpendicular bisector?

• A line that intersects a segment at a 90-degree angle and divides it into two equal parts

• A line that is parallel to another line

• A line that intersects a segment at any angle

• A line that divides an angle into two equal parts

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, what can be said about its distance to the endpoints of the segment?

• It is not related to the endpoints

• It is farther from both endpoints

• It is equidistant from both endpoints

• It is closer to one endpoint than the other

In the converse of the perpendicular bisector theorem, if a point is equidistant from the endpoints of a segment, where does it lie?

• On the angle bisector of the segment

• On the perpendicular bisector of the segment

• On a parallel line to the segment

• On the segment itself

If the distance from point A to point C is 9 units, what is the distance from point A to point B, given that line AD is the perpendicular bisector of segment BC?

• Cannot be determined

• 18 units

• 9 units

• 4.5 units

What does an angle bisector do to an angle?

• Makes the angle larger

• Divides it into two unequal parts

• Makes the angle smaller

• Divides it into two congruent adjacent angles

According to the angle bisector theorem, if a point lies on the bisector of an angle, what can be said about its distance to the sides of the angle?

• It is farther from both sides

• It is not related to the sides

• It is closer to one side than the other

• It is equidistant from both sides

In the converse of the angle bisector theorem, if a point is equidistant from the two sides of an angle, where does it lie?

• On one of the sides

• On a parallel line to one of the sides

• On the angle bisector

• Outside the angle

If the measure of angle CAD is 20 degrees, what is the measure of angle CAB, given that D is equidistant to C and B?

• 80 degrees

• 40 degrees

• 20 degrees

• 60 degrees

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

• Finding the slope of the segment

• Finding the midpoint of the segment

• Finding the y-intercept

• Finding the length of the segment

If the slope of a segment is 1/2, what is the slope of its perpendicular bisector?

• -2

• 1/2

• -1/2

• 2