Perpendicular Bisectors and Angle Bisectors

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

What is an angle bisector?

Back

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

Front

How can you determine if a point lies on the perpendicular bisector of a segment?

Back

A point lies on the perpendicular bisector if it is equidistant from the endpoints of the segment.

Front

What is the relationship between the perpendicular bisector and the segment it bisects?

Back

The perpendicular bisector is always perpendicular to the segment and intersects it at its midpoint.

Front

If point C is on the perpendicular bisector of segment AB, what can be said about the distances AC and BC?

Back

The distances AC and BC are equal.

Front

How do you find the length of a segment given its endpoints?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the angle bisector in triangle geometry?

Back

The angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.

Front

If two angles are bisected, what can be said about the measures of the resulting angles?

Back

The measures of the resulting angles are equal.

Front

What is the relationship between the lengths of segments created by an angle bisector?

Back

The lengths of the segments created by an angle bisector are proportional to the lengths of the other two sides of the triangle.

Front

How do you find the measure of an angle if you know the measures of its bisected angles?

Back

Add the measures of the two bisected angles together.