Exploring Perpendicular and Angle Bisectors

The video tutorial covers the concepts of perpendicular and angle bisectors, explaining the perpendicular bisector theorem and its converse. It demonstrates how a point on a perpendicular bisector is equidistant from the segment's endpoints. The tutorial also explores the angle bisector theorem, showing that a point on an angle bisector is equidistant from the sides of the angle. Examples and proofs are provided to illustrate these geometric principles.

What is a perpendicular bisector?

• A line that is parallel to a segment.

• A line that divides a segment into three equal parts.

• A line that intersects a segment at its midpoint and forms a 90-degree angle.

• A line that intersects a segment at any point.

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

• The point is on the line connecting the two objects.

• The point is closer to one object than the other.

• The point is the same distance from both objects.

• The point is farther from both objects.

According to the Perpendicular Bisector Theorem, if a point is on the perpendicular bisector of a segment, it is:

• On the segment itself.

• Farther from the endpoints of the segment.

• Equidistant from the endpoints of the segment.

• Closer to one endpoint of the segment.

In the Perpendicular Bisector Theorem, if AP = 5, what is PB?

• 15

• 5

• 0

• 10

What does the Converse of the Perpendicular Bisector Theorem state?

• If a point is on the segment, it is equidistant from the endpoints.

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

• If a point is equidistant from the endpoints, it is on the segment.

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

In the diagram, if PQ is the perpendicular bisector of CD, what can be said about CP and DP?

• CP is greater than DP.

• CP is less than DP.

• CP is equal to DP.

• CP and DP are unrelated.

How do you solve for x in the equation 6x - 1 = 3x + 8?

• x = 1

• x = 2

• x = 3

• x = 4

What is the Angle Bisector Theorem?

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

• If a point is on the bisector of an angle, it is closer to one side of the angle.

• If a point is on the bisector of an angle, it is farther from one side of the angle.

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

In the Angle Bisector Theorem, if SP is perpendicular to QP and SR is perpendicular to QR, what can be said about SP and SR?

• SP is equal to SR.

• SP is greater than SR.

• SP and SR are unrelated.

• SP is less than SR.

What does the Converse of the Angle Bisector Theorem state?

• If a point is equidistant from the sides of an angle, it is closer to one side.

• If a point is equidistant from the sides of an angle, it is farther from one side.

• If a point is equidistant from the sides of an angle, it is on the angle itself.

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