Equidistant Points and Bisectors

The video tutorial covers perpendicular and angle bisectors, including definitions, theorems, and examples. It explains the perpendicular bisector theorem and its converse, as well as the angle bisector theorem and its converse. The tutorial provides problem-solving examples and guides students on writing the equation of a perpendicular bisector using point-slope form.

What are the two main learning targets discussed in the introduction?

• Proving and applying theorems about perpendicular and angle bisectors

• Calculating the area of triangles

• Understanding parallel lines and their properties

• Identifying different types of angles

What does it mean for a point to be equidistant from two objects?

• The point is the same distance from both objects

• The point is on the line connecting the two objects

• The point is at the midpoint of the segment connecting the objects

• The point is closer to one object than the other

How is a perpendicular bisector defined?

• A set of points equidistant from the endpoints of a segment

• A line that is parallel to a given segment

• A line that intersects a segment at its midpoint

• 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 concluded?

• The point is closer to one endpoint than the other

• The point is on the segment itself

• The point is equidistant from the endpoints of the segment

• The point is at the midpoint of the segment

In the example problem, what is the length of segment MN if NP is the perpendicular bisector of ML?

• 3.2

• 4.0

• 2.6

• 5.1

What is the Angle Bisector Theorem?

• A point on the bisector of an angle is equidistant from the sides of the angle

• A point on the bisector of an angle is at the midpoint of the angle

• A point on the bisector of an angle is on the angle itself

• A point on the bisector of an angle is closer to one side than the other

In the example problem, what is the measure of angle EFH if angle EFG is 50° and EF is the bisector?

• 25°

• 35°

• 20°

• 30°

What is the first step in writing an equation for the perpendicular bisector of a segment?

• Find the slope of the segment

• Find the angle of the segment

• Find the midpoint of the segment

• Find the length of the segment

What is the slope of the perpendicular bisector if the slope of the segment is 3/2?

• -2/3

• 2/3

• 3/2

• -3/2

What is the final form of the equation for the perpendicular bisector in the example?

• y - 2 = 3/2(x + 8)

• y = 2/3(x - 8)

• y + 2 = -2/3(x - 8)

• y = -3/2(x + 8)