Perpendicular Bisector and Angle Bisector Theorem

Front

What is a perpendicular bisector?

Back

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

Front

State the Perpendicular Bisector Theorem.

Back

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

Front

What is an angle bisector?

Back

An angle bisector is a ray that divides an angle into two equal angles.

Front

State the Angle Bisector Theorem.

Back

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

Front

How do you find the length of a segment using the Perpendicular Bisector Theorem?

Back

Use the theorem to establish that the distances from the point on the bisector to the endpoints are equal, then solve for the unknown length.

Front

What is the relationship between angles formed by perpendicular bisectors?

Back

The angles formed by perpendicular bisectors are right angles (90 degrees).

Front

If a point is 5 units from one endpoint of a segment, what is its distance from the other endpoint if it lies on the perpendicular bisector?

Back

The distance from the other endpoint is also 5 units.

Front

How can you determine if a point lies on the angle bisector?

Back

Measure the distances from the point to each side of the angle; if they are equal, the point lies on the angle bisector.

Front

What is the measure of angles formed by an angle bisector if the original angle is 80 degrees?

Back

Each of the two angles formed will measure 40 degrees.

Front

If two segments are bisected perpendicularly, what can be said about their lengths?

Back

The lengths of the segments are equal if they are bisected by the same perpendicular bisector.