Exploring Perpendicular and Angle Bisectors

This video tutorial covers lesson 6-2 on perpendicular and angle bisectors. It begins with definitions of key terms such as equidistant, perpendicular bisector, and angle bisector. The video then explains and proves the perpendicular bisector theorem and its converse, followed by the angle bisector theorem. Algebraic examples are provided to apply these theorems, and a coordinate plane example demonstrates how to find a perpendicular bisector using midpoint and slope calculations.

What does the term 'equidistant' refer to?

• A point that is the same distance from two or more objects

• A line that is perpendicular to a segment

• A ray that splits an angle into two congruent angles

• The shortest distance from a point to a line

What is the shortest distance from a point to a line?

• A straight path

• A curved path

• A diagonal path

• A perpendicular path

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, it is:

• At the midpoint of the segment

• Closer to one endpoint

• On the segment

• Equidistant from the endpoints

What is required to prove that a line is a perpendicular bisector according to the converse of the perpendicular bisector theorem?

• The midpoint of the segment

• Three points on the line

• Two points equidistant from the endpoints

• One point equidistant from the endpoints

In the proof of the perpendicular bisector theorem, which property is used to show that XY is congruent to XY?

• Reflexive property

• Substitution property

• Transitive property

• Symmetric property

What does the angle bisector theorem state?

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

• An angle bisector splits an angle into two unequal parts

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

• An angle bisector is perpendicular to the sides of the angle

If a point is equidistant from the sides of an angle, what can be concluded?

• The point is on one side of the angle

• The point is on the angle bisector

• The point is at the vertex of the angle

• The point is outside the angle

In the algebraic example, if UW is given as 7x + 13 and XU is a perpendicular bisector, what is the length of UW when x = 6?

• 48

• 55

• 60

• 42

In the angle bisector example, if FG is given as x + 11 and x = 5, what is the length of FG?

• 17

• 14

• 15

• 16

What is the slope of the perpendicular bisector if the original line has a slope of 3/2?

• -2/3

• 2/3

• 3/2

• -3/2