Perpendicular Bisector and Angle Bisector Theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that if a point is on the angle bisector of an angle, then it is equidistant from the two sides of the angle.

Front

How do you find the measure of an angle using the Angle Bisector Theorem?

Back

To find the measure of an angle using the Angle Bisector Theorem, you can set up a proportion based on the lengths of the segments created by the angle bisector.

Front

What does it mean for a line to be a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If a point lies on the perpendicular bisector of a segment, what can you say about its distances to the endpoints?

Back

The distances from the point to the endpoints of the segment are equal.

Front

What is the relationship between angles formed by a perpendicular bisector and the segment it bisects?

Back

The angles formed by a perpendicular bisector and the segment it bisects are right angles (90 degrees).

Front

How can you use the Angle Bisector Theorem to solve for unknown lengths?

Back

You can use the Angle Bisector Theorem to set up a proportion between the lengths of the segments created by the angle bisector to solve for unknown lengths.

Front

What is the formula for finding the length of a segment using the Perpendicular Bisector Theorem?

Back

The length of the segment can be found using the distance formula, or by using the properties of right triangles formed by the perpendicular bisector.

Front

If two angles are bisected, what can you say about the measures of the resulting angles?

Back

The measures of the resulting angles are equal to half of the measure of the original angle.

Front

What is the significance of the point where the perpendicular bisector intersects a segment?

Back

The intersection point is the midpoint of the segment, and it is equidistant from both endpoints.